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

Modeling cardiomyocyte signaling and metabolism predicts genotype-to-phenotype mechanisms in hypertrophic cardiomyopathy

Familial hypertrophic cardiomyopathy (HCM) is a significant precursor of heart failure and sudden cardiac death, primarily caused by mutations in sarcomeric and structural proteins. Despite the extensive research on the HCM genotype, the complex and context-specific nature of many signaling and metabolic pathways linking the HCM genotype to phenotype has hindered therapeutic advancements for patients. Here, we have developed a computational model of HCM encompassing cardiomyocyte signaling and metabolic networks and their associated interactions. Utilizing a stochastic logic-based ODE approach, we linked cardiomyocyte signaling to the metabolic network through a gene regulatory network and post-translational modifications. We validated the model against published data on activities of signaling species in the HCM context and transcriptomes of two HCM mouse models (i.e., R403Q-αMyHC and R92W-TnT). Our model predicts that HCM mutation induces changes in metabolic functions such as ATP synthase deficiency and a transition from fatty acids to carbohydrate metabolism. The model indicated major shifts in glutamine-related metabolism and increased apoptosis after HCM-induced ATP synthase deficiency. We predicted that the transcription factors STAT, SRF, GATA4, TP53, and FoxO are the key regulators of cardiomyocyte hypertrophy and apoptosis in HCM in alignment with experiments. Moreover, we identified shared (e.g., activation of PGC1α by AMPK, and FHL1 by titin) and context-specific mechanisms (e.g., regulation of Ca2+ sensitivity by titin in HCM patients) that may control genotype-to-phenotype transition in HCM across different species or mutations. We also predicted potential combination drug targets for HCM (e.g., mavacamten plus ROS inhibitors) preventing or reversing HCM phenotype (i.e., hypertrophic growth, apoptosis, and metabolic remodeling) in cardiomyocytes. This study provides new insights into mechanisms linking genotype to phenotype in familial hypertrophic cardiomyopathy and offers a framework for assessing new treatments and exploring variations in HCM experimental models.

Biologically informed NeuralODEs for genome-wide regulatory dynamics

BACKGROUND

Gene regulatory network (GRN) models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such gene regulatory ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the underlying GRN governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impede either scalability, explainability, or both.

RESULTS

We developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that overcomes limitations of other methods by flexibly incorporating prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of GRN ODEs. We tested the accuracy of PHOENIX in a series of in silico experiments, benchmarking it against several currently used tools. We demonstrated PHOENIX's flexibility by modeling regulation of oscillating expression profiles obtained from synchronized yeast cells. We also assessed the scalability of PHOENIX by modeling genome-scale GRNs for breast cancer samples ordered in pseudotime and for B cells treated with Rituximab.

CONCLUSIONS

PHOENIX uses a combination of user-defined prior knowledge and functional forms from systems biology to encode biological "first principles" as soft constraints on the GRN allowing us to predict subsequent gene expression patterns in a biologically explainable manner.

A Graphical Approach to Visualize and Interpret Biochemically Coupled Biomechanical Models

The last decade has seen the emergence of progressively more complex mechanobiological models, often coupling biochemical and biomechanical components. The complexity of these models makes interpretation difficult, and although computational tools can solve model equations, there is considerable potential value in a simple method to explore the interplay between different model components. Pump and system performance curves, long utilized in centrifugal pump selection and design, inspire the development of a graphical technique to depict visually the performance of biochemically-coupled mechanical models. Our approach is based on a biochemical performance curve (analogous to the classical pump curve) and a biomechanical performance curve (analogous to the system curve). Upon construction of the two curves, their intersection, or lack thereof, describes the coupled model's equilibrium state(s). One can also observe graphically how an applied perturbation shifts one or both curves, and thus how the other component will respond, without rerunning the full model. While the upfront cost of generating the performance curve graphic varies with the efficiency of the model components, the easily interpretable visual depiction of what would otherwise be nonintuitive model behavior is valuable. Herein, we outline how performance curves can be constructed and interpreted for biochemically-coupled biomechanical models and apply the technique to two independent models in the cardiovascular space. The performance curve approach can illustrate and help identify weaknesses in model construction, inform user-applied perturbations and fitting procedures to generate intended behaviors, and improve the efficiency of the model generation and application process.

Multiscale computational model of aortic remodeling following postnatal disruption of TGFβ signaling

The healthy adult aorta is a remarkably resilient structure, able to resist relentless cardiac-induced and hemodynamic loads under normal conditions. Fundamental to such mechanical homeostasis is the mechano-sensitive cell signaling that controls gene products and thus the structural integrity of the wall. Mouse models have shown that smooth muscle cell-specific disruption of transforming growth factor-beta (TGFβ) signaling during postnatal development compromises this resiliency, rendering the aortic wall susceptible to aneurysm and dissection under normal mechanical loading. By contrast, disruption of such signaling in the adult aorta appears to introduce a vulnerability that remains hidden under normal loading, but manifests under increased loading as experienced during hypertension. We present a multiscale (transcript to tissue) computational model to examine possible reasons for compromised mechanical homeostasis in the adult aorta following reduced TGFβ signaling in smooth muscle cells.

Multiscale computational model predicts how environmental changes and drug treatments affect microvascular remodeling in fibrotic disease

Investigating the molecular, cellular, and tissue-level changes caused by disease, and the effects of pharmacological treatments across these biological scales, necessitates the use of multiscale computational modeling in combination with experimentation. Many diseases dynamically alter the tissue microenvironment in ways that trigger microvascular network remodeling, which leads to the expansion or regression of microvessel networks. When microvessels undergo remodeling in idiopathic pulmonary fibrosis (IPF), functional gas exchange is impaired due to loss of alveolar structures and lung function declines. Here, we integrated a multiscale computational model with independent experiments to investigate how combinations of biomechanical and biochemical cues in IPF alter cell fate decisions leading to microvascular remodeling. Our computational model predicted that extracellular matrix (ECM) stiffening reduced microvessel area, which was accompanied by physical uncoupling of endothelial cell (ECs) and pericytes, the cells that comprise microvessels. Nintedanib, an FDA-approved drug for treating IPF, was predicted to further potentiate microvessel regression by decreasing the percentage of quiescent pericytes while increasing the percentage of pericytes undergoing pericyte-myofibroblast transition (PMT) in high ECM stiffnesses. Importantly, the model suggested that YAP/TAZ inhibition may overcome the deleterious effects of nintedanib by promoting EC-pericyte coupling and maintaining microvessel homeostasis. Overall, our combination of computational and experimental modeling can explain how cell decisions affect tissue changes during disease and in response to treatments.

Divergent iron-regulatory states contribute to heterogeneity in breast cancer aggressiveness

Primary tumors with similar mutational profiles can progress to vastly different outcomes where transcriptional state, rather than mutational profile, predicts prognosis. A key challenge is to understand how distinct tumor cell states are induced and maintained. In triple negative breast cancer cells, invasive behaviors and aggressive transcriptional signatures linked to poor patient prognosis can emerge in response to contact with collagen type I. Herein, collagen-induced migration heterogeneity within a TNBC cell line was leveraged to identify transcriptional programs associated with invasive versus non-invasive phenotypes and implicate molecular switches. Phenotype-guided sequencing revealed that invasive cells upregulate iron uptake and utilization machinery, anapleurotic TCA cycle genes, actin polymerization promoters, and a distinct signature of Rho GTPase activity and contractility regulating genes. The non-invasive cell state is characterized by actin and iron sequestration modules along with glycolysis gene expression. These unique tumor cell states are evident in patient tumors and predict divergent outcomes for TNBC patients. Glucose tracing confirmed that non-invasive cells are more glycolytic than invasive cells, and functional studies in cell lines and PDO models demonstrated a causal relationship between phenotype and metabolic state. Mechanistically, the OXPHOS dependent invasive state resulted from transient HO-1 upregulation triggered by contact with dense collagen that reduced heme levels and mitochondrial chelatable iron levels. This induced expression of low cytoplasmic iron response genes regulated by ACO1/IRP1. Knockdown or inhibition of HO-1, ACO1/IRP1, MRCK, or OXPHOS abrogated invasion. These findings support an emerging theory that heme and iron flux serve as important regulators of TNBC aggressiveness.

Logic-based mechanistic machine learning on high-content images reveals how drugs differentially regulate cardiac fibroblasts

Fibroblasts are essential regulators of extracellular matrix deposition following cardiac injury. These cells exhibit highly plastic responses in phenotype during fibrosis in response to environmental stimuli. Here, we test whether and how candidate anti-fibrotic drugs differentially regulate measures of cardiac fibroblast phenotype, which may help identify treatments for cardiac fibrosis. We conducted a high-content microscopy screen of human cardiac fibroblasts treated with 13 clinically relevant drugs in the context of TGFβ and/or IL-1β, measuring phenotype across 137 single-cell features. We used the phenotypic data from our high-content imaging to train a logic-based mechanistic machine learning model (LogiMML) for fibroblast signaling. The model predicted how pirfenidone and Src inhibitor WH-4-023 reduce actin filament assembly and actin-myosin stress fiber formation, respectively. Validating the LogiMML model prediction that PI3K partially mediates the effects of Src inhibition, we found that PI3K inhibition reduces actin-myosin stress fiber formation and procollagen I production in human cardiac fibroblasts. In this study, we establish a modeling approach combining the strengths of logic-based network models and regularized regression models. We apply this approach to predict mechanisms that mediate the differential effects of drugs on fibroblasts, revealing Src inhibition acting via PI3K as a potential therapy for cardiac fibrosis.

Logic-based modeling of biological networks with Netflux

Molecular signaling networks drive a diverse range of cellular decisions, including whether to proliferate, how and when to die, and many processes in between. Such networks often connect hundreds of proteins, genes, and processes. Understanding these complex networks is greatly aided by computational modeling, but these tools require extensive programming knowledge. In this article, we describe a user-friendly, programming-free network simulation tool called Netflux (https://github.com/saucermanlab/Netflux). Over the last decade, Netflux has been used to construct numerous predictive network models that have deepened our understanding of how complex biological networks make cell decisions. Here, we provide a Netflux tutorial that covers how to construct a network model and then simulate network responses to perturbations. Upon completion of this tutorial, you will be able to construct your own model in Netflux and simulate how perturbations to proteins and genes propagate through signaling and gene-regulatory networks.

Physiological Indirect Response Model to Omics-Powered Quantitative Systems Pharmacology Model

Over the past several decades, mathematical modeling has been applied to increasingly wider scopes of questions in drug development. Accordingly, the range of modeling tools has also been evolving, as showcased by contributions of Jusko and colleagues: from basic pharmacokinetics/pharmacodynamics (PK/PD) modeling to today's platform-based approach of quantitative systems pharmacology (QSP) modeling. Aimed at understanding the mechanism of action of investigational drugs, QSP models characterize systemic effects by incorporating information about cellular signaling networks, which is often represented by omics data. In this perspective, we share a few examples illustrating approaches for the integration of omics into mechanistic QSP modeling. We briefly overview how the evolution of PK/PD modeling into QSP has been accompanied by an increase in available data and the complexity of mathematical methods that integrate it. We discuss current gaps and challenges of integrating omics data into QSP models and propose several potential areas where integrated QSP and omics modeling may benefit drug development.

Logic-Based Modeling of Inflammatory Macrophage Crosstalk with Glomerular Endothelial Cells in Diabetic Kidney Disease

Diabetic kidney disease is a complication in 1 out of 3 patients with diabetes. Aberrant glucose metabolism in diabetes leads to an immune response causing inflammation and to structural and functional damage in the glomerular cells of the kidney. Complex cellular signaling lies at the core of metabolic and functional derangement. Unfortunately, the mechanism underlying the role of inflammation in glomerular endothelial cell dysfunction during diabetic kidney disease is not fully understood. Computational models in systems biology allow the integration of experimental evidence and cellular signaling networks to understand mechanisms involved in disease progression. We built a logic-based ordinary differential equations model to study macrophage-dependent inflammation in glomerular endothelial cells during diabetic kidney disease progression. We studied the crosstalk between macrophages and glomerular endothelial cells in the kidney using a protein signaling network stimulated with glucose and lipopolysaccharide. The network and model were built using the open-source software package Netflux. This modeling approach overcomes the complexity of studying network models and the need for extensive mechanistic details. The model simulations were fitted and validated against available biochemical data from in vitro experiments. The model identified mechanisms responsible for dysregulated signaling in macrophages and glomerular endothelial cells during diabetic kidney disease. In addition, we investigated the influence of signaling interactions and species that on glomerular endothelial cell morphology through selective knockdown and downregulation. We found that partial knockdown of VEGF receptor 1, PLC-γ, adherens junction proteins, and calcium partially recovered the endothelial cell fenestration size. Our model findings contribute to understanding signaling and molecular perturbations that affect the glomerular endothelial cells in the early stage of diabetic kidney disease.

Logic-based mechanistic machine learning on high-content images reveals how drugs differentially regulate cardiac fibroblasts

Fibroblasts are essential regulators of extracellular matrix deposition following cardiac injury. These cells exhibit highly plastic responses in phenotype during fibrosis in response to environmental stimuli. Here, we test whether and how candidate anti-fibrotic drugs differentially regulate measures of cardiac fibroblast phenotype, which may help identify treatments for cardiac fibrosis. We conducted a high content microscopy screen of human cardiac fibroblasts treated with 13 clinically relevant drugs in the context of TGFβ and/or IL-1β, measuring phenotype across 137 single-cell features. We used the phenotypic data from our high content imaging to train a logic-based mechanistic machine learning model (LogiMML) for fibroblast signaling. The model predicted how pirfenidone and Src inhibitor WH-4-023 reduce actin filament assembly and actin-myosin stress fiber formation, respectively. Validating the LogiMML model prediction that PI3K partially mediates the effects of Src inhibition, we found that PI3K inhibition reduces actin-myosin stress fiber formation and procollagen I production in human cardiac fibroblasts. In this study, we establish a modeling approach combining the strengths of logic-based network models and regularized regression models, apply this approach to predict mechanisms that mediate the differential effects of drugs on fibroblasts, revealing Src inhibition acting via PI3K as a potential therapy for cardiac fibrosis.

Computational screen for sex-specific drug effects in a cardiac fibroblast signaling network model

Heart disease is the leading cause of death in both men and women. Cardiac fibrosis is the uncontrolled accumulation of extracellular matrix proteins, which can exacerbate the progression of heart failure, and there are currently no drugs approved specifically to target matrix accumulation in the heart. Computational signaling network models (SNMs) can be used to facilitate discovery of novel drug targets. However, the vast majority of SNMs are not sex-specific and/or are developed and validated using data skewed towards male in vitro and in vivo samples. Biological sex is an important consideration in cardiovascular health and drug development. In this study, we integrate a cardiac fibroblast SNM with estrogen signaling pathways to create sex-specific SNMs. The sex-specific SNMs demonstrated high validation accuracy compared to in vitro experimental studies in the literature while also elucidating how estrogen signaling can modulate the effect of fibrotic cytokines via multi-pathway interactions. Further, perturbation analysis and drug screening uncovered several drug compounds predicted to generate divergent fibrotic responses in male vs. female conditions, which warrant further study in the pursuit of sex-specific treatment recommendations for cardiac fibrosis. Future model development and validation will require more generation of sex-specific data to further enhance modeling capabilities for clinically relevant sex-specific predictions of cardiac fibrosis and treatment.

A computational bridge between traction force microscopy and tissue contraction

Arterial wall active mechanics are driven by resident smooth muscle cells, which respond to biological, chemical, and mechanical stimuli and activate their cytoskeletal machinery to generate contractile stresses. The cellular mechanoresponse is sensitive to environmental perturbations, often leading to maladaptation and disease progression. When investigated at the single cell scale, however, these perturbations do not consistently result in phenotypes observed at the tissue scale. Here, a multiscale model is introduced that translates microscale contractility signaling into a macroscale, tissue-level response. The microscale framework incorporates a biochemical signaling network along with characterization of fiber networks that govern the anisotropic mechanics of vascular tissue. By incorporating both biochemical and mechanical components, the model is more flexible and more broadly applicable to physiological and pathological conditions. The model can be applied to both cell and tissue scale systems, allowing for the analysis of in vitro, traction force microscopy and ex vivo, isometric contraction experiments in parallel. When applied to aortic explant rings and isolated smooth muscle cells, the model predicts that active contractility is not a function of stretch at intermediate strain. The model also successfully predicts cell-scale and tissue-scale contractility and matches experimentally observed behaviors, including the hypercontractile phenotype caused by chronic hyperglycemia. The connection of the microscale framework to the macroscale through the multiscale model presents a framework that can translate the wealth of information already collected at the cell scale to tissue scale phenotypes, potentially easing the development of smooth muscle cell-targeting therapeutics.

Vascular smooth muscle cell mechanotransduction through serum and glucocorticoid inducible kinase-1 promotes interleukin-6 production and macrophage accumulation in murine hypertension

Objective

The objective of this investigation was to demonstrate that in vivo induction of hypertension (HTN) and in vitro cyclic stretch of aortic vascular smooth muscle cells (VSMCs) can cause serum and glucocorticoid-inducible kinase (SGK-1)-dependent production of cytokines to promote macrophage accumulation that may promote vascular pathology.

Methods

HTN was induced in C57Bl/6 mice with angiotensin II infusion (1.46 mg/kg/day × 21 days) with or without systemic infusion of EMD638683 (2.5 mg/kg/day × 21 days), a selective SGK-1 inhibitor. Systolic blood pressure was recorded. Abdominal aortas were harvested to quantify SGK-1 activity (pSGK-1/SGK-1) by immunoblot. Flow cytometry quantified the abundance of CD11b+/F480+ cells (macrophages). Plasma interleukin (IL)-6 and monocyte chemoattractant protein-1 (MCP-1) was assessed by enzyme-linked immunosorbent assay. Aortic VSMCs from wild-type mice were subjected to 12% biaxial cyclic stretch (Stretch) for 3 or 12 hours with or without EMD638683 (10 μM) and with or without SGK-1 small interfering RNA with subsequent quantitative polymerase chain reaction for IL-6 and MCP-1 expression. IL-6 and MCP-1 in culture media were analyzed by enzyme-linked immunosorbent assay. Aortic VSMCs from SGK-1flox+/+ mice were transfected with Cre-Adenovirus to knockdown SGK-1 (SGK-1KD VSMCs) and underwent parallel tension experimentation. Computational modeling was used to simulate VSMC signaling. Statistical analysis included analysis of variance with significance at a P value of <.05.

Results

SGK-1 activity, abundance of CD11b+/F4-80+ cells, and plasma IL-6 were increased in the abdominal aorta of mice with HTN and significantly reduced by treatment with EMD638683. This outcome mirrored the increased abundance of IL-6 in media from Stretch C57Bl/6 VSMCs and attenuation of the effect with EMD638683 or SGK-1 small interfering RNA. C57Bl/6 VSMCs also responded to Stretch with increased MCP-1 expression and secretion into the culture media. Further supporting the integral role of mechanical signaling through SGK-1, target gene expression and cytokine secretion was unchanged in SGK-1KD VSMCs with Stretch, and computer modeling confirmed SGK-1 as an intersecting node of signaling owing to mechanical strain and angiotensin II.

Conclusions

Mechanical activation of SGK-1 in aortic VSMCs can promote inflammatory signaling and increased macrophage abundance, therefore this kinase warrants further exploration as a pharmacotherapeutic target to abrogate hypertensive vascular pathology.

Persistent non-homeostatic remodeling of aortic collagen following a brief episode of hypertension: A computational study

The healthy adult aorta exhibits a remarkable homeostatic ability to respond to sustained changes in hemodynamic loads under many circumstances, but this mechanical homeostasis can be compromised or lost in natural aging and diverse pathological processes. Herein, we investigate persistent non-homeostatic changes in the composition and mechanical properties of the thoracic aorta in adult wild-type mice following 14 days of angiotensin II-induced hypertension. We employ a multiscale computational model of arterial growth and remodeling driven by mechanosensitive and angiotensin II-related cell signaling pathways. We find that experimentally observed findings can only be recapitulated computationally if the collagen deposited during the transient period of hypertension has altered properties (deposition stretch, fiber angle, crosslinking) compared with the collagen produced in the original homeostatic state. Some of these changes are predicted to persist for at least six months after blood pressure is restored to normal levels, consistent with the experimental findings.

A structural bio-chemo-mechanical model for vascular smooth muscle cell traction force microscopy

Altered vascular smooth muscle cell (VSMC) contractility is both a response to and a driver for impaired arterial function, and the leading experimental technique for quantifying VSMC contraction is traction force microscopy (TFM). TFM involves the complex interaction among several chemical, biological, and mechanical mechanisms, making it difficult to translate TFM results into tissue-scale behavior. Here, a computational model capturing each of the major aspects of the cell traction process is presented. The model incorporates four interacting components: a biochemical signaling network, individual actomyosin fiber bundle contraction, a cytoskeletal network of interconnected fibers, and elastic substrate displacement due to cytoskeletal force. The synthesis of these four components leads to a broad, flexible framework for describing TFM and linking biochemical and biomechanical phenomena on the single-cell level. The model recapitulated available data on VSMCs following biochemical, geometric, and mechanical perturbations. The structural bio-chemo-mechanical model offers a tool to interpret TFM data in new, more mechanistic ways, providing a framework for the evaluation of new biological hypotheses, interpolation of new data, and potential translation from single-cell experiments to multi-scale tissue models.

The Microenvironment of the Pathogenesis of Cardiac Hypertrophy

Pathological cardiac hypertrophy is a key risk factor for the development of heart failure and predisposes individuals to cardiac arrhythmia and sudden death. While physiological cardiac hypertrophy is adaptive, hypertrophy resulting from conditions comprising hypertension, aortic stenosis, or genetic mutations, such as hypertrophic cardiomyopathy, is maladaptive. Here, we highlight the essential role and reciprocal interactions involving both cardiomyocytes and non-myocardial cells in response to pathological conditions. Prolonged cardiovascular stress causes cardiomyocytes and non-myocardial cells to enter an activated state releasing numerous pro-hypertrophic, pro-fibrotic, and pro-inflammatory mediators such as vasoactive hormones, growth factors, and cytokines, i.e., commencing signaling events that collectively cause cardiac hypertrophy. Fibrotic remodeling is mediated by cardiac fibroblasts as the central players, but also endothelial cells and resident and infiltrating immune cells enhance these processes. Many of these hypertrophic mediators are now being integrated into computational models that provide system-level insights and will help to translate our knowledge into new pharmacological targets. This perspective article summarizes the last decades' advances in cardiac hypertrophy research and discusses the herein-involved complex myocardial microenvironment and signaling components.

Network model integrated with multi-omic data predicts MBNL1 signals that drive myofibroblast activation

RNA-binding protein muscleblind-like1 (MBNL1) was recently identified as a central regulator of cardiac wound healing and myofibroblast activation. To identify putative MBNL1 targets, we integrated multiple genome-wide screens with a fibroblast network model. We expanded the model to include putative MBNL1-target interactions and recapitulated published experimental results to validate new signaling modules. We prioritized 14 MBNL1 targets and developed novel fibroblast signaling modules for p38 MAPK, Hippo, Runx1, and Sox9 pathways. We experimentally validated MBNL1 regulation of p38 expression in mouse cardiac fibroblasts. Using the expanded fibroblast model, we predicted a hierarchy of MBNL1 regulated pathways with strong influence on αSMA expression. This study lays a foundation to explore the network mechanisms of MBNL1 signaling central to fibrosis.

Computational Screen for Sex-Specific Drug Effects in a Cardiac Fibroblast Network Model

Heart disease is the leading cause of death in both men and women. Cardiac fibrosis is the uncontrolled accumulation of extracellular matrix proteins which can exacerbate the progression of heart failure, and there are currently no drugs approved specifically to target matrix accumulation in the heart. Computational signaling network models (SNMs) can be used to facilitate discovery of novel drug targets. However, the vast majority of SNMs are not sex-specific and/or are developed and validated using data skewed towards male in vitro and in vivo samples. Biological sex is an important consideration in cardiovascular health and drug development. In this study, we integrate a previously constructed cardiac fibroblast SNM with estrogen signaling pathways to create sex-specific SNMs. The sex-specific SNMs maintained previously high validation when compared to in vitro experimental studies in the literature. A sex-specific perturbation analysis and drug screen uncovered several potential pathways that warrant further study in the pursuit of sex-specific treatment recommendations for cardiac fibrosis.

Biologically informed NeuralODEs for genome-wide regulatory dynamics

Models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the causal gene-regulatory network (GRN) governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impedes scalability and/or explainability. To overcome these limitations, we developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that can flexibly incorporate prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of ODEs. We test accuracy of PHOENIX in a series of in silico experiments benchmarking it against several currently used tools for ODE estimation. We also demonstrate PHOENIX's flexibility by studying oscillating expression data from synchronized yeast cells and assess its scalability by modelling genome-scale breast cancer expression for samples ordered in pseudotime. Finally, we show how the combination of user-defined prior knowledge and functional forms from systems biology allows PHOENIX to encode key properties of the underlying GRN, and subsequently predict expression patterns in a biologically explainable way.

Design principles of improving the dose-response alignment in coupled GTPase switches

"Dose-response alignment" (DoRA), where the downstream response of cellular signaling pathways closely matches the fraction of activated receptor, can improve the fidelity of dose information transmission. The negative feedback has been experimentally identified as a key component for DoRA, but numerical simulations indicate that negative feedback is not sufficient to achieve perfect DoRA, i.e., perfect match of downstream response and receptor activation level. Thus a natural question is whether there exist design principles for signaling motifs within only negative feedback loops to improve DoRA to near-perfect DoRA. Here, we investigated several model formulations of an experimentally validated circuit that couples two molecular switches-mGTPase (monomeric GTPase) and tGTPase (heterotrimeric GTPases) - with negative feedback loops. In the absence of feedback, the low and intermediate mGTPase activation levels benefit DoRA in mass action and Hill-function models, respectively. Adding negative feedback has versatile roles on DoRA: it may impair DoRA in the mass action model with low mGTPase activation level and Hill-function model with intermediate mGTPase activation level; in other cases, i.e., the mass action model with a high mGTPase activation level or the Hill-function model with a non-intermediate mGTPase activation level, it improves DoRA. Furthermore, we found that DoRA in a longer cascade (i.e., tGTPase) can be obtained using Hill-function kinetics under certain conditions. In summary, we show how ranges of activity of mGTPase, reaction kinetics, the negative feedback, and the cascade length affect DoRA. This work provides a framework for improving the DoRA performance in signaling motifs with negative feedback.

Understanding How Cells Probe the World: A Preliminary Step towards Modeling Cell Behavior?

Cell biologists have long aimed at quantitatively modeling cell function. Recently, the outstanding progress of high-throughput measurement methods and data processing tools has made this a realistic goal. The aim of this paper is twofold: First, to suggest that, while much progress has been done in modeling cell states and transitions, current accounts of environmental cues driving these transitions remain insufficient. There is a need to provide an integrated view of the biochemical, topographical and mechanical information processed by cells to take decisions. It might be rewarding in the near future to try to connect cell environmental cues to physiologically relevant outcomes rather than modeling relationships between these cues and internal signaling networks. The second aim of this paper is to review exogenous signals that are sensed by living cells and significantly influence fate decisions. Indeed, in addition to the composition of the surrounding medium, cells are highly sensitive to the properties of neighboring surfaces, including the spatial organization of anchored molecules and substrate mechanical and topographical properties. These properties should thus be included in models of cell behavior. It is also suggested that attempts at cell modeling could strongly benefit from two research lines: (i) trying to decipher the way cells encode the information they retrieve from environment analysis, and (ii) developing more standardized means of assessing the quality of proposed models, as was done in other research domains such as protein structure prediction.

Signaling network model of cardiomyocyte morphological changes in familial cardiomyopathy

Familial cardiomyopathy is a precursor of heart failure and sudden cardiac death. Over the past several decades, researchers have discovered numerous gene mutations primarily in sarcomeric and cytoskeletal proteins causing two different disease phenotypes: hypertrophic (HCM) and dilated (DCM) cardiomyopathies. However, molecular mechanisms linking genotype to phenotype remain unclear. Here, we employ a systems approach by integrating experimental findings from preclinical studies (e.g., murine data) into a cohesive signaling network to scrutinize genotype to phenotype mechanisms. We developed an HCM/DCM signaling network model utilizing a logic-based differential equations approach and evaluated model performance in predicting experimental data from four contexts (HCM, DCM, pressure overload, and volume overload). The model has an overall prediction accuracy of 83.8%, with higher accuracy in the HCM context (90%) than DCM (75%). Global sensitivity analysis identifies key signaling reactions, with calcium-mediated myofilament force development and calcium-calmodulin kinase signaling ranking the highest. A structural revision analysis indicates potential missing interactions that primarily control calcium regulatory proteins, increasing model prediction accuracy. Combination pharmacotherapy analysis suggests that downregulation of signaling components such as calcium, titin and its associated proteins, growth factor receptors, ERK1/2, and PI3K-AKT could inhibit myocyte growth in HCM. In experiments with patient-specific iPSC-derived cardiomyocytes (MLP-W4R;MYH7-R723C iPSC-CMs), combined inhibition of ERK1/2 and PI3K-AKT rescued the HCM phenotype, as predicted by the model. In DCM, PI3K-AKT-NFAT downregulation combined with upregulation of Ras/ERK1/2 or titin or Gq protein could ameliorate cardiomyocyte morphology. The model results suggest that HCM mutations that increase active force through elevated calcium sensitivity could increase ERK activity and decrease eccentricity through parallel growth factors, Gq-mediated, and titin pathways. Moreover, the model simulated the influence of existing medications on cardiac growth in HCM and DCM contexts. This HCM/DCM signaling model demonstrates utility in investigating genotype to phenotype mechanisms in familial cardiomyopathy.

Intracellular signaling control of mechanical homeostasis in the aorta

Mature arteries exhibit a preferred biomechanical state in health evidenced by a narrow range of intramural and wall shear stresses. When stresses are perturbed by changes in blood pressure or flow, homeostatic mechanisms tend to restore target values via altered contractility and/or cell and matrix turnover. In contrast, vascular disease associates with compromised homeostasis, hence we must understand mechanisms underlying mechanical homeostasis and its robustness. Here, we use a multiscale computational model wherein mechanosensitive intracellular signaling pathways drive arterial growth and remodeling. First, we identify an ensemble of cell-level parameterizations where tissue-level responses are well-regulated and adaptive to hemodynamic perturbations. The responsible mechanism is persistent multiscale negative feedback whereby mechanosensitive signaling drives mass turnover until homeostatic target stresses are reached. This demonstrates how robustness emerges despite inevitable cell and individual heterogeneity. Second, we investigate tissue-level effects of signaling node knockdowns (ATIR, ROCK, TGF[Formula: see text]RII, PDGFR, ERK1/2) and find general agreement with experimental reports of fault tolerance. Robustness against structural changes manifests via low engagement of the node under baseline stresses or compensatory multiscale feedback via upregulation of additional pathways. Third, we show how knockdowns affect collagen and smooth muscle turnover at baseline and with perturbed stresses. In several cases, basal production is not remarkably affected, but sensitivities to stress deviations, which influence feedback strength, are reduced. Such reductions can impair adaptive responses, consistent with previously reported aortic vulnerability despite grossly normal appearances. Reduced stress sensitivities thus form a candidate mechanism for how robustness is lost, enabling transitions from health towards disease.

Multiscale model of heart growth during pregnancy: integrating mechanical and hormonal signaling

Pregnancy stands at the interface of mechanics and biology. The growing fetus continuously loads the maternal organs as circulating hormone levels surge, leading to significant changes in mechanical and hormonal cues during pregnancy. In response, maternal soft tissues undergo remarkable growth and remodeling to support the mother and baby for a healthy pregnancy. We focus on the maternal left ventricle, which increases its cardiac output and mass during pregnancy. This study develops a multiscale cardiac growth model for pregnancy to understand how mechanical and hormonal cues interact to drive this growth process. We coupled a cell signaling network model that predicts cell-level hypertrophy in response to hormones and stretch to a compartmental model of the rat heart and circulation that predicts organ-level growth in response to hemodynamic changes. We calibrated this multiscale model to data from experimental volume overload and hormonal infusions of angiotensin 2 (AngII), estrogen (E2), and progesterone (P4). We then validated the model's ability to capture interactions between inputs by comparing model predictions against published observations for the combinations of VO + E2 and AngII + E2. Finally, we simulated pregnancy-induced changes in hormones and hemodynamics to predict heart growth during pregnancy. Our model produced growth consistent with experimental data. Overall, our analysis suggests that the rise in P4 during the first half of gestation is an important contributor to heart growth during pregnancy. We conclude with suggestions for future experimental studies that will provide a better understanding of how hormonal and mechanical cues interact to drive pregnancy-induced heart growth.

Computational model of brain endothelial cell signaling pathways predicts therapeutic targets for cerebral pathologies

Brain endothelial cells serve many critical homeostatic functions. In addition to sensing and regulating blood flow, they maintain blood-brain barrier function, including precise control of nutrient exchange and efflux of xenobiotics. Many signaling pathways in brain endothelial cells have been implicated in both health and disease; however, our understanding of how these signaling pathways functionally integrate is limited. A model capable of integrating these signaling pathways could both advance our understanding of brain endothelial cell signaling networks and potentially identify promising molecular targets for endothelial cell-based drug or gene therapies. To this end, we developed a large-scale computational model, wherein brain endothelial cell signaling pathways were reconstructed from the literature and converted into a network of logic-based differential equations. The model integrates 63 nodes (including proteins, mRNA, small molecules, and cell phenotypes) and 82 reactions connecting these nodes. Specifically, our model combines signaling pathways relating to VEGF-A, BDNF, NGF, and Wnt signaling, in addition to incorporating pathways relating to focused ultrasound as a therapeutic delivery tool. To validate the model, independently established relationships between selected inputs and outputs were simulated, with the model yielding correct predictions 73% of the time. We identified influential and sensitive nodes under different physiological or pathological contexts, including altered brain endothelial cell conditions during glioma, Alzheimer's disease, and ischemic stroke. Nodes with the greatest influence over combinations of desired model outputs were identified as potential druggable targets for these disease conditions. For example, the model predicts therapeutic benefits from inhibiting AKT, Hif-1α, or cathepsin D in the context of glioma - each of which are currently being studied in clinical or pre-clinical trials. Notably, the model also permits testing multiple combinations of node alterations for their effects on the network and the desired outputs (such as inhibiting AKT and overexpressing the P75 neurotrophin receptor simultaneously in the context of glioma), allowing for the prediction of optimal combination therapies. In all, our approach integrates results from over 100 past studies into a coherent and powerful model, capable of both revealing network interactions unapparent from studying any one pathway in isolation and predicting therapeutic targets for treating devastating brain pathologies.

Network modeling predicts personalized gene expression and drug responses in valve myofibroblasts cultured with patient sera

Aortic valve stenosis (AVS) patients experience pathogenic valve leaflet stiffening due to excessive extracellular matrix (ECM) remodeling. Numerous microenvironmental cues influence pathogenic expression of ECM remodeling genes in tissue-resident valvular myofibroblasts, and the regulation of complex myofibroblast signaling networks depends on patient-specific extracellular factors. Here, we combined a manually curated myofibroblast signaling network with a data-driven transcription factor network to predict patient-specific myofibroblast gene expression signatures and drug responses. Using transcriptomic data from myofibroblasts cultured with AVS patient sera, we produced a large-scale, logic-gated differential equation model in which 11 biochemical and biomechanical signals were transduced via a network of 334 signaling and transcription reactions to accurately predict the expression of 27 fibrosis-related genes. Correlations were found between personalized model-predicted gene expression and AVS patient echocardiography data, suggesting links between fibrosis-related signaling and patient-specific AVS severity. Further, global network perturbation analyses revealed signaling molecules with the most influence over network-wide activity, including endothelin 1 (ET1), interleukin 6 (IL6), and transforming growth factor β (TGFβ), along with downstream mediators c-Jun N-terminal kinase (JNK), signal transducer and activator of transcription (STAT), and reactive oxygen species (ROS). Lastly, we performed virtual drug screening to identify patient-specific drug responses, which were experimentally validated via fibrotic gene expression measurements in valvular interstitial cells cultured with AVS patient sera and treated with or without bosentan-a clinically approved ET1 receptor inhibitor. In sum, our work advances the ability of computational approaches to provide a mechanistic basis for clinical decisions including patient stratification and personalized drug screening.

Fibroblast mechanotransduction network predicts targets for mechano-adaptive infarct therapies

Regional control of fibrosis after myocardial infarction is critical for maintaining structural integrity in the infarct while preventing collagen accumulation in non-infarcted areas. Cardiac fibroblasts modulate matrix turnover in response to biochemical and biomechanical cues, but the complex interactions between signaling pathways confound efforts to develop therapies for regional scar formation. We employed a logic-based ordinary differential equation model of fibroblast mechano-chemo signal transduction to predict matrix protein expression in response to canonical biochemical stimuli and mechanical tension. Functional analysis of mechano-chemo interactions showed extensive pathway crosstalk with tension amplifying, dampening, or reversing responses to biochemical stimuli. Comprehensive drug target screens identified 13 mechano-adaptive therapies that promote matrix accumulation in regions where it is needed and reduce matrix levels in regions where it is not needed. Our predictions suggest that mechano-chemo interactions likely mediate cell behavior across many tissues and demonstrate the utility of multi-pathway signaling networks in discovering therapies for context-specific disease states.

From data to QSP models: a pipeline for using Boolean networks for hypothesis inference and dynamic model building

Quantitative Systems Pharmacology (QSP) models capture the physiological underpinnings driving the response to a drug and express those in a semi-mechanistic way, often involving ordinary differential equations (ODEs). The process of developing a QSP model generally starts with the definition of a set of reasonable hypotheses that would support a mechanistic interpretation of the expected response which are used to form a network of interacting elements. This is a hypothesis-driven and knowledge-driven approach, relying on prior information about the structure of the network. However, with recent advances in our ability to generate large datasets rapidly, often in a hypothesis-neutral manner, the opportunity emerges to explore data-driven approaches to establish the network topologies and models in a robust, repeatable manner. In this paper, we explore the possibility of developing complex network representations of physiological responses to pharmaceuticals using a logic-based analysis of available data and then convert the logic relations to dynamic ODE-based models. We discuss an integrated pipeline for converting data to QSP models. This pipeline includes using k-means clustering to binarize continuous data, inferring likely network relationships using a Best-Fit Extension method to create a Boolean network, and finally converting the Boolean network to a continuous ODE model. We utilized an existing QSP model for the dual-affinity re-targeting antibody flotetuzumab to demonstrate the robustness of the process. Key output variables from the QSP model were used to generate a continuous data set for use in the pipeline. This dataset was used to reconstruct a possible model. This reconstruction had no false-positive relationships, and the output of each of the species was similar to that of the original QSP model. This demonstrates the ability to accurately infer relationships in a hypothesis-neutral manner without prior knowledge of a system using this pipeline.

Brahma safeguards canalization of cardiac mesoderm differentiation

Differentiation proceeds along a continuum of increasingly fate-restricted intermediates, referred to as canalization^1,2. Canalization is essential for stabilizing cell fate, but the mechanisms that underlie robust canalization are unclear. Here we show that the BRG1/BRM-associated factor (BAF) chromatin-remodelling complex ATPase gene Brm safeguards cell identity during directed cardiogenesis of mouse embryonic stem cells. Despite the establishment of a well-differentiated precardiac mesoderm, Brm^-/- cells predominantly became neural precursors, violating germ layer assignment. Trajectory inference showed a sudden acquisition of a non-mesodermal identity in Brm^-/- cells. Mechanistically, the loss of Brm prevented de novo accessibility of primed cardiac enhancers while increasing the expression of neurogenic factor POU3F1, preventing the binding of the neural suppressor REST and shifting the composition of BRG1 complexes. The identity switch caused by the Brm mutation was overcome by increasing BMP4 levels during mesoderm induction. Mathematical modelling supports these observations and demonstrates that Brm deletion affects cell fate trajectory by modifying saddle-node bifurcations². In the mouse embryo, Brm deletion exacerbated mesoderm-deleted Brg1-mutant phenotypes, severely compromising cardiogenesis, and reveals an in vivo role for Brm. Our results show that Brm is a compensable safeguard of the fidelity of mesoderm chromatin states, and support a model in which developmental canalization is not a rigid irreversible path, but a highly plastic trajectory.

Roles of mTOR in thoracic aortopathy understood by complex intracellular signaling interactions

Thoracic aortopathy–aneurysm, dissection, and rupture–is increasingly responsible for significant morbidity and mortality. Advances in medical genetics and imaging have improved diagnosis and thus enabled earlier prophylactic surgical intervention in many cases. There remains a pressing need, however, to understand better the underlying molecular and cellular mechanisms with the hope of finding robust pharmacotherapies. Diverse studies in patients and mouse models of aortopathy have revealed critical changes in multiple smooth muscle cell signaling pathways that associate with disease, yet integrating information across studies and models has remained challenging. We present a new quantitative network model that includes many of the key smooth muscle cell signaling pathways and validate the model using a detailed data set that focuses on hyperactivation of the mechanistic target of rapamycin (mTOR) pathway and its inhibition using rapamycin. We show that the model can be parameterized to capture the primary experimental findings both qualitatively and quantitatively. We further show that simulating a population of cells by varying receptor reaction weights leads to distinct proteomic clusters within the population, and that these clusters emerge due to a bistable switch driven by positive feedback in the PI3K/AKT/mTOR signaling pathway.

Cell signaling drives changes across scales, from altered transcription at the single-cell level to tissue-level growth and remodeling. Studying complex interactions within cell signaling pathways can lead to a better understanding of the progression of disease. In particular, we are interested in how vascular cells can change their phenotype in a way that exacerbates aortopathy, namely, the development of aneurysms, dissections, and rupture. In this study we built a novel cell signaling network model of a vascular smooth muscle cell using archival data and used it to capture the effects of a genetic knock-out and subsequent pharmacologic rescue. We then used the model to simulate populations of smooth muscle cells and found that small perturbations to the strength of signaling can lead to distinct clusters of cells. With further analysis of the network substructures, we found that a positive feedback loop within the network was responsible for the distinct phenotypes we saw in our clusters of simulated cells. We believe that this work not only helps us to understand changes in smooth muscle cell phenotype but also opens the possibility to study other signaling perturbations associated with aortopathy.

Network model-based screen for FDA-approved drugs affecting cardiac fibrosis

Cardiac fibrosis is a significant component of pathological heart remodeling, yet it is not directly targeted by existing drugs. Systems pharmacology approaches have the potential to provide mechanistic frameworks with which to predict and understand how drugs modulate biological systems. Here, we combine network modeling of the fibroblast signaling network with 36 unique drug-target interactions from DrugBank to predict drugs that modulate fibroblast phenotype and fibrosis. Galunisertib was predicted to decrease collagen and α-SMA expression, which we validated in human cardiac fibroblasts. In vivo fibrosis data from the literature validated predictions for 10 drugs. Further, the model was used to identify network mechanisms by which these drugs work. Arsenic trioxide was predicted to induce fibrosis by AP1-driven TGFβ expression and MMP2-driven TGFβ activation. Entresto (valsartan/sacubitril) was predicted to suppress fibrosis by valsartan suppression of ERK signaling and sacubitril enhancement of PKG activity, both of which decreased Smad3 activity. Overall, this study provides a framework for integrating drug-target mechanisms with logic-based network models, which can drive further studies both in cardiac fibrosis and other conditions.

Computational model of cardiomyocyte apoptosis identifies mechanisms of tyrosine kinase inhibitor-induced cardiotoxicity

Despite clinical observations of cardiotoxicity among cancer patients treated with tyrosine kinase inhibitors (TKIs), the molecular mechanisms by which these drugs affect the heart remain largely unknown. Mechanistic understanding of TKI-induced cardiotoxicity has been limited in part due to the complexity of tyrosine kinase signaling pathways and the multi-targeted nature of many of these drugs. TKI treatment has been associated with reactive oxygen species generation, mitochondrial dysfunction, and apoptosis in cardiomyocytes. To gain insight into the mechanisms mediating TKI-induced cardiotoxicity, this study constructs and validates a computational model of cardiomyocyte apoptosis, integrating intrinsic apoptotic and tyrosine kinase signaling pathways. The model predicts high levels of apoptosis in response to sorafenib, sunitinib, ponatinib, trastuzumab, and gefitinib, and lower levels of apoptosis in response to nilotinib and erlotinib, with the highest level of apoptosis induced by sorafenib. Knockdown simulations identified AP1, ASK1, JNK, MEK47, p53, and ROS as positive functional regulators of sorafenib-induced apoptosis of cardiomyocytes. Overexpression simulations identified Akt, IGF1, PDK1, and PI3K among the negative functional regulators of sorafenib-induced cardiomyocyte apoptosis. A combinatorial screen of the positive and negative regulators of sorafenib-induced apoptosis revealed ROS knockdown coupled with overexpression of FLT3, FGFR, PDGFR, VEGFR, or KIT as a particularly potent combination in reducing sorafenib-induced apoptosis. Network simulations of combinatorial treatment with sorafenib and the antioxidant N-acetyl cysteine (NAC) suggest that NAC may protect cardiomyocytes from sorafenib-induced apoptosis.

Network Analysis Reveals a Distinct Axis of Macrophage Activation in Response to Conflicting Inflammatory Cues

Macrophages are subject to a wide range of cytokine and pathogen signals in vivo, which contribute to differential activation and modulation of inflammation. Understanding the response to multiple, often-conflicting cues that macrophages experience requires a network perspective. In this study, we integrate data from literature curation and mRNA expression profiles obtained from wild type C57/BL6J mice macrophages to develop a large-scale computational model of the macrophage signaling network. In response to stimulation across all pairs of nine cytokine inputs, the model predicted activation along the classic M1-M2 polarization axis but also a second axis of macrophage activation that distinguishes unstimulated macrophages from a mixed phenotype induced by conflicting cues. Along this second axis, combinations of conflicting stimuli, IL-4 with LPS, IFN-γ, IFN-β, or TNF-α, produced mutual inhibition of several signaling pathways, e.g., NF-κB and STAT6, but also mutual activation of the PI3K signaling module. In response to combined IFN-γ and IL-4, the model predicted genes whose expression was mutually inhibited, e.g., iNOS or Nos2 and Arg1, or mutually enhanced, e.g., Il4rα and Socs1, validated by independent experimental data. Knockdown simulations further predicted network mechanisms underlying functional cross-talk, such as mutual STAT3/STAT6-mediated enhancement of Il4rα expression. In summary, the computational model predicts that network cross-talk mediates a broadened spectrum of macrophage activation in response to mixed pro- and anti-inflammatory cytokine cues, making it useful for modeling in vivo scenarios.

From Transcript to Tissue: Multiscale Modeling from Cell Signaling to Matrix Remodeling

Tissue-level biomechanical properties and function derive from underlying cell signaling, which regulates mass deposition, organization, and removal. Here, we couple two existing modeling frameworks to capture associated multiscale interactions-one for vessel-level growth and remodeling and one for cell-level signaling-and illustrate utility by simulating aortic remodeling. At the vessel level, we employ a constrained mixture model describing turnover of individual wall constituents (elastin, intramural cells, and collagen), which has proven useful in predicting diverse adaptations as well as disease progression using phenomenological constitutive relations. Nevertheless, we now seek an improved mechanistic understanding of these processes; we replace phenomenological relations in the mixture model with a logic-based signaling model, which yields a system of ordinary differential equations predicting changes in collagen synthesis, matrix metalloproteinases, and cell proliferation in response to altered intramural stress, wall shear stress, and exogenous angiotensin II. This coupled approach promises improved understanding of the role of cell signaling in achieving tissue homeostasis and allows us to model feedback between vessel mechanics and cell signaling. We verify our model predictions against data from the hypertensive murine infrarenal abdominal aorta as well as results from validated phenomenological models, and consider effects of noisy signaling and heterogeneous cell populations.

Context-specific network modeling identifies new crosstalk in β-adrenergic cardiac hypertrophy

Cardiac hypertrophy is a context-dependent phenomenon wherein a myriad of biochemical and biomechanical factors regulate myocardial growth through a complex large-scale signaling network. Although numerous studies have investigated hypertrophic signaling pathways, less is known about hypertrophy signaling as a whole network and how this network acts in a context-dependent manner. Here, we developed a systematic approach, CLASSED (Context-specific Logic-bASed Signaling nEtwork Development), to revise a large-scale signaling model based on context-specific data and identify main reactions and new crosstalks regulating context-specific response. CLASSED involves four sequential stages with an automated validation module as a core which builds a logic-based ODE model from the interaction graph and outputs the model validation percent. The context-specific model is developed by estimation of default parameters, classified qualitative validation, hybrid Morris-Sobol global sensitivity analysis, and discovery of missing context-dependent crosstalks. Applying this pipeline to our prior-knowledge hypertrophy network with context-specific data revealed key signaling reactions which distinctly regulate cell response to isoproterenol, phenylephrine, angiotensin II and stretch. Furthermore, with CLASSED we developed a context-specific model of β-adrenergic cardiac hypertrophy. The model predicted new crosstalks between calcium/calmodulin-dependent pathways and upstream signaling of Ras in the ISO-specific context. Experiments in cardiomyocytes validated the model’s predictions on the role of CaMKII-Gβγ and CaN-Gβγ interactions in mediating hypertrophic signals in ISO-specific context and revealed a difference in the phosphorylation magnitude and translocation of ERK1/2 between cardiac myocytes and fibroblasts. CLASSED is a systematic approach for developing context-specific large-scale signaling networks, yielding insights into new-found crosstalks in β-adrenergic cardiac hypertrophy.

Pathological cardiac hypertrophy is a disease in which the heart grows abnormally in response to different motivators such as high blood pressure or variations in hormones and growth factors. The shape of the heart after its growth depends on the context in which it grows. Since cell signaling in the cardiac cells plays a key role in the determination of heart shape, a thorough understanding of cardiac cells signaling in each context enlightens the mechanisms which control response of cardiac cells. However, cell signaling in cardiac hypertrophy comprises a complex web of pathways with numerous interactions, and predicting how these interactions control the hypertrophic signal in each context is not achievable by only experiments or general computational models. To address this need, we developed an approach to bring together the experimental data of each context with a signaling network curated from literature to identify the main players of cardiac cells response in each context and attain the context-specific models of cardiac hypertrophy. By utilizing our approach, we identified the main regulators of cardiac hypertrophy in four important contexts. We developed a network model of β-adrenergic cardiac hypertrophy, and predicted and validated new interactions that regulate cardiac cells response in this context.

Computational model predicts paracrine and intracellular drivers of fibroblast phenotype after myocardial infarction

The fibroblast is a key mediator of wound healing in the heart and other organs, yet how it integrates multiple time-dependent paracrine signals to control extracellular matrix synthesis has been difficult to study in vivo. Here, we extended a computational model to simulate the dynamics of fibroblast signaling and fibrosis after myocardial infarction (MI) in response to time-dependent data for nine paracrine stimuli. This computational model was validated against dynamic collagen expression and collagen area fraction data from post-infarction rat hearts. The model predicted that while many features of the fibroblast phenotype at inflammatory or maturation phases of healing could be recapitulated by single static paracrine stimuli (interleukin-1 and angiotensin-II, respectively), mimicking the reparative phase required paired stimuli (e.g. TGFβ and endothelin-1). Virtual overexpression screens simulated with either static cytokine pairs or post-MI paracrine dynamic predicted phase-specific regulators of collagen expression. Several regulators increased (Smad3) or decreased (Smad7, protein kinase G) collagen expression specifically in the reparative phase. NADPH oxidase (NOX) overexpression sustained collagen expression from reparative to maturation phases, driven by TGFβ and endothelin positive feedback loops. Interleukin-1 overexpression had mixed effects, both enhancing collagen via the TGFβ positive feedback loop and suppressing collagen via NFκB and BAMBI (BMP and activin membrane-bound inhibitor) incoherent feed-forward loops. These model-based predictions reveal network mechanisms by which the dynamics of paracrine stimuli and interacting signaling pathways drive the progression of fibroblast phenotypes and fibrosis after myocardial infarction.

Cell signaling model for arterial mechanobiology

Arterial growth and remodeling at the tissue level is driven by mechanobiological processes at cellular and sub-cellular levels. Although it is widely accepted that cells seek to promote tissue homeostasis in response to biochemical and biomechanical cues—such as increased wall stress in hypertension—the ways by which these cues translate into tissue maintenance, adaptation, or maladaptation are far from understood. In this paper, we present a logic-based computational model for cell signaling within the arterial wall, aiming to predict changes in extracellular matrix turnover and cell phenotype in response to pressure-induced wall stress, flow-induced wall shear stress, and exogenous sources of angiotensin II, with particular interest in mouse models of hypertension. We simulate a number of experiments from the literature at both the cell and tissue level, involving single or combined inputs, and achieve high qualitative agreement in most cases. Additionally, we demonstrate the utility of this modeling approach for simulating alterations (in this case knockdowns) of individual nodes within the signaling network. Continued modeling of cellular signaling will enable improved mechanistic understanding of arterial growth and remodeling in health and disease, and will be crucial when considering potential pharmacological interventions.

Biological soft tissues are characterized by continuous production and removal of material, which endows them with a remarkable ability to adapt to changes in their biochemical and biomechanical environments. For arteries, mechanical stimuli result primarily from changes in blood pressure or flow, and biochemical changes are induced by multiple factors, including pharmacological intervention. In order to understand how arterial properties are maintained in health, or how they adapt or fail to adapt in disease, we must understand better how these diverse stimuli affect material turnover. Extracellular matrix is tightly regulated by mechano-sensing and mechano-regulation, and therefore cell signaling, thus we present a computational model of relevant signaling pathways within the vascular wall, with the aim of predicting changes in wall composition and function in response to three main inputs: pressure-induced wall stress, flow-induced wall shear stress, and exogenous angiotensin II. We obtain qualitative agreement with a range of experimental studies from the literature, and provide illustrative examples demonstrating how such models can be used to further our understanding of arterial remodeling.

Quantification of model and data uncertainty in a network analysis of cardiac myocyte mechanosignalling

Cardiac myocytes transduce changes in mechanical loading into cellular responses via interacting cell signalling pathways. We previously reported a logic-based ordinary differential equation model of the myocyte mechanosignalling network that correctly predicts 78% of independent experimental results not used to formulate the original model. Here, we use Monte Carlo and polynomial chaos expansion simulations to examine the effects of uncertainty in parameter values, model logic and experimental validation data on the assessed accuracy of that model. The prediction accuracy of the model was robust to parameter changes over a wide range being least sensitive to uncertainty in time constants and most affected by uncertainty in reaction weights. Quantifying epistemic uncertainty in the reaction logic of the model showed that while replacing 'OR' with 'AND' reactions greatly reduced model accuracy, replacing 'AND' with 'OR' reactions was more likely to maintain or even improve accuracy. Finally, data uncertainty had a modest effect on assessment of model accuracy. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Quantification of uncertainty in a new network model of pulmonary arterial adventitial fibroblast pro-fibrotic signalling

Here, we present a novel network model of the pulmonary arterial adventitial fibroblast (PAAF) that represents seven signalling pathways, confirmed to be important in pulmonary arterial fibrosis, as 92 reactions and 64 state variables. Without optimizing parameters, the model correctly predicted 80% of 39 results of input-output and inhibition experiments reported in 20 independent papers not used to formulate the original network. Parameter uncertainty quantification (UQ) showed that this measure of model accuracy is robust to changes in input weights and half-maximal activation levels (EC50), but is more affected by uncertainty in the Hill coefficient (n), which governs the biochemical cooperativity or steepness of the sigmoidal activation function of each state variable. Epistemic uncertainty in model structure, due to the reliance of some network components and interactions on experiments using non-PAAF cell types, suggested that this source of uncertainty had a smaller impact on model accuracy than the alternative of reducing the network to only those interactions reported in PAAFs. UQ highlighted model parameters that can be optimized to improve prediction accuracy and network modules where there is the greatest need for new experiments. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Differential co-expression-based detection of conditional relationships in transcriptional data: comparative analysis and application to breast cancer

BACKGROUND

Elucidation of regulatory networks, including identification of regulatory mechanisms specific to a given biological context, is a key aim in systems biology. This has motivated the move from co-expression to differential co-expression analysis and numerous methods have been developed subsequently to address this task; however, evaluation of methods and interpretation of the resulting networks has been hindered by the lack of known context-specific regulatory interactions.

RESULTS

In this study, we develop a simulator based on dynamical systems modelling capable of simulating differential co-expression patterns. With the simulator and an evaluation framework, we benchmark and characterise the performance of inference methods. Defining three different levels of "true" networks for each simulation, we show that accurate inference of causation is difficult for all methods, compared to inference of associations. We show that a z-score-based method has the best general performance. Further, analysis of simulation parameters reveals five network and simulation properties that explained the performance of methods. The evaluation framework and inference methods used in this study are available in the dcanr R/Bioconductor package.

CONCLUSIONS

Our analysis of networks inferred from simulated data show that hub nodes are more likely to be differentially regulated targets than transcription factors. Based on this observation, we propose an interpretation of the inferred differential network that can reconstruct a putative causal network.

Towards perturbation prediction of biological networks using deep learning

The mapping of the physical interactions between biochemical entities enables quantitative analysis of dynamic biological living systems. While developing a precise dynamical model on biological entity interaction is still challenging due to the limitation of kinetic parameter detection of the underlying biological system. This challenge promotes the needs of topology-based models to predict biochemical perturbation patterns. Pure topology-based model, however, is limited on the scale and heterogeneity of biological networks. Here we propose a learning based model that adopts graph convolutional networks to learn the implicit perturbation pattern factors and thus enhance the perturbation pattern prediction on the basic topology model. Our experimental studies on 87 biological models show an average of 73% accuracy on perturbation pattern prediction and outperforms the best topology-based model by 7%, indicating that the graph-driven neural network model is robust and beneficial for accurate prediction of the perturbation spread modeling and giving an inspiration of the implementation of the deep neural networks on biological network modeling.

Predicting perturbation patterns from the topology of biological networks

High-throughput technologies, offering an unprecedented wealth of quantitative data underlying the makeup of living systems, are changing biology. Notably, the systematic mapping of the relationships between biochemical entities has fueled the rapid development of network biology, offering a suitable framework to describe disease phenotypes and predict potential drug targets. However, our ability to develop accurate dynamical models remains limited, due in part to the limited knowledge of the kinetic parameters underlying these interactions. Here, we explore the degree to which we can make reasonably accurate predictions in the absence of the kinetic parameters. We find that simple dynamically agnostic models are sufficient to recover the strength and sign of the biochemical perturbation patterns observed in 87 biological models for which the underlying kinetics are known. Surprisingly, a simple distance-based model achieves 65% accuracy. We show that this predictive power is robust to topological and kinetic parameter perturbations, and we identify key network properties that can increase up to 80% the recovery rate of the true perturbation patterns. We validate our approach using experimental data on the chemotactic pathway in bacteria, finding that a network model of perturbation spreading predicts with ∼80% accuracy the directionality of gene expression and phenotype changes in knock-out and overproduction experiments. These findings show that the steady advances in mapping out the topology of biochemical interaction networks opens avenues for accurate perturbation spread modeling, with direct implications for medicine and drug development.

Discrete dynamic network modeling of oncogenic signaling: Mechanistic insights for personalized treatment of cancer

Targeted drugs disrupting proteins that are dysregulated in cancer have emerged as promising treatments because of their specificity to cancer cell aberrations and thus their improved side effect profile. However, their success remains limited, largely due to existing or emergent therapy resistance. We suggest that this is due to limited understanding of the entire relevant cellular landscape. A class of mathematical models called discrete dynamic network models can be used to understand the integrated effect of an individual tumor's aberrations. We review the recent literature on discrete dynamic models of cancer and highlight their predicted therapeutic strategies. We believe dynamic network modeling can be used to drive treatment decision-making in a personalized manner to direct improved treatments in cancer.

•

Cancer is rooted in incorrect cellular decisions caused by genetic alterations.

•

Dynamic models of signaling networks can map the relevant repertoire of alterations.

•

Discrete dynamic network models can predict therapeutic interventions.

•

Progress in personalized medicine needs integration of multiple data and model types.

Target Control in Logical Models Using the Domain of Influence of Nodes

Dynamical models of biomolecular networks are successfully used to understand the mechanisms underlying complex diseases and to design therapeutic strategies. Network control and its special case of target control, is a promising avenue toward developing disease therapies. In target control it is assumed that a small subset of nodes is most relevant to the system's state and the goal is to drive the target nodes into their desired states. An example of target control would be driving a cell to commit to apoptosis (programmed cell death). From the experimental perspective, gene knockout, pharmacological inhibition of proteins, and providing sustained external signals are among practical intervention techniques. We identify methodologies to use the stabilizing effect of sustained interventions for target control in Boolean network models of biomolecular networks. Specifically, we define the domain of influence (DOI) of a node (in a certain state) to be the nodes (and their corresponding states) that will be ultimately stabilized by the sustained state of this node regardless of the initial state of the system. We also define the related concept of the logical domain of influence (LDOI) of a node, and develop an algorithm for its identification using an auxiliary network that incorporates the regulatory logic. This way a solution to the target control problem is a set of nodes whose DOI can cover the desired target node states. We perform greedy randomized adaptive search in node state space to find such solutions. We apply our strategy to in silico biological network models of real systems to demonstrate its effectiveness.

Boolean network modeling in systems pharmacology

Quantitative systems pharmacology (QSP) is an emerging discipline that aims to discover how drugs modulate the dynamics of biological components in molecular and cellular networks and the impact of those perturbations on human pathophysiology. The integration of systems-based experimental and computational approaches is required to facilitate the advancement of this field. QSP models typically consist of a series of ordinary differential equations (ODE). However, this mathematical framework requires extensive knowledge of parameters pertaining to biological processes, which is often unavailable. An alternative framework that does not require knowledge of system-specific parameters, such as Boolean network modeling, could serve as an initial foundation prior to the development of an ODE-based model. Boolean network models have been shown to efficiently describe, in a qualitative manner, the complex behavior of signal transduction and gene/protein regulatory processes. In addition to providing a starting point prior to quantitative modeling, Boolean network models can also be utilized to discover novel therapeutic targets and combinatorial treatment strategies. Identifying drug targets using a network-based approach could supplement current drug discovery methodologies and help to fill the innovation gap across the pharmaceutical industry. In this review, we discuss the process of developing Boolean network models and the various analyses that can be performed to identify novel drug targets and combinatorial approaches. An example for each of these analyses is provided using a previously developed Boolean network of signaling pathways in multiple myeloma. Selected examples of Boolean network models of human (patho-)physiological systems are also reviewed in brief.

Predictive model identifies key network regulators of cardiomyocyte mechano-signaling

Mechanical strain is a potent stimulus for growth and remodeling in cells. Although many pathways have been implicated in stretch-induced remodeling, the control structures by which signals from distinct mechano-sensors are integrated to modulate hypertrophy and gene expression in cardiomyocytes remain unclear. Here, we constructed and validated a predictive computational model of the cardiac mechano-signaling network in order to elucidate the mechanisms underlying signal integration. The model identifies calcium, actin, Ras, Raf1, PI3K, and JAK as key regulators of cardiac mechano-signaling and characterizes crosstalk logic imparting differential control of transcription by AT1R, integrins, and calcium channels. We find that while these regulators maintain mostly independent control over distinct groups of transcription factors, synergy between multiple pathways is necessary to activate all the transcription factors necessary for gene transcription and hypertrophy. We also identify a PKG-dependent mechanism by which valsartan/sacubitril, a combination drug recently approved for treating heart failure, inhibits stretch-induced hypertrophy, and predict further efficacious pairs of drug targets in the network through a network-wide combinatorial search.

Common stresses such as high blood pressure or heart attack can lead to heart failure, which afflicts over 25 million people worldwide. These stresses cause cardiomyocytes to grow and remodel, which may initially be beneficial but ultimately worsen heart function. Current heart failure drugs such as beta-blockers counteract biochemical cues prompting cardiomyocyte growth, yet mechanical cues to cardiomyocytes such as stretch are just as important in driving cardiac dysfunction. However, no pharmacological treatments have yet been approved that specifically target mechano-signaling, in part because it is not clear how cardiomyocytes integrate signals from multiple mechano-responsive sensors and pathways into their decision to grow. To address this challenge, we built a systems-level computational model that represents 125 interactions between 94 stretch-responsive signaling molecules. The model correctly predicts 134 of 172 previous independent experimental observations, and identifies the key regulators of stretch-induced cardiomyocyte remodeling. Although cardiomyocytes have many mechano-signaling pathways that function largely independently, we find that cooperation between them is necessary to cause growth and remodeling. We identify mechanisms by which a recently approved heart failure drug pair affects mechano-signaling, and we further predict additional pairs of drug targets that could be used to help reverse heart failure.

Integrated Strategies to Gain a Systems-Level View of Dynamic Signaling Networks

In order to survive and function properly in the face of an ever changing environment, cells must be able to sense changes in their surroundings and respond accordingly. Cells process information about their environment through complex signaling networks composed of many discrete signaling molecules. Individual pathways within these networks are often tightly integrated and highly dynamic, allowing cells to respond to a given stimulus (or, as is typically the case under physiological conditions, a combination of stimuli) in a specific and appropriate manner. However, due to the size and complexity of many cellular signaling networks, it is often difficult to predict how cellular signaling networks will respond under a particular set of conditions. Indeed, crosstalk between individual signaling pathways may lead to responses that are nonintuitive (or even counterintuitive) based on examination of the individual pathways in isolation. Therefore, to gain a more comprehensive view of cell signaling processes, it is important to understand how signaling networks behave at the systems level. This requires integrated strategies that combine quantitative experimental data with computational models. In this chapter, we first examine some of the progress that has recently been made toward understanding the systems-level regulation of cellular signaling networks, with a particular emphasis on phosphorylation-dependent signaling networks. We then discuss how genetically targetable fluorescent biosensors are being used together with computational models to gain unique insights into the spatiotemporal regulation of signaling networks within single, living cells.

Current Trends in Multidrug Optimization: An Alley of Future Successful Treatment of Complex Disorders

The identification of effective and long-lasting cancer therapies still remains elusive, partially due to patient and tumor heterogeneity, acquired drug resistance, and single-drug dose-limiting toxicities. The use of drug combinations may help to overcome some limitations of current cancer therapies by challenging the robustness and redundancy of biological processes. However, effective drug combination optimization requires the careful consideration of numerous parameters. The complexity of this optimization problem is clearly nontrivial and likely requires the assistance of advanced heuristic optimization techniques. In the current review, we discuss the application of optimization techniques for the identification of optimal drug combinations. More specifically, we focus on the application of phenotype-based screening approaches in the field of cancer therapy. These methods are divided into three categories: (1) modeling methods, (2) model-free approaches based on biological search algorithms, and (3) merged approaches, particularly phenotypically driven network biology methods and computation network models relying on phenotypic data. In addition to a brief description of each approach, we include a critical discussion of the advantages and disadvantages of each method, with a strong focus on the limitations and considerations needed to successfully apply such methods in biological research.

Current Trends in Multidrug Optimization

The identification of effective and long-lasting cancer therapies still remains elusive, partially due to patient and tumor heterogeneity, acquired drug resistance, and single-drug dose-limiting toxicities. The use of drug combinations may help to overcome some limitations of current cancer therapies by challenging the robustness and redundancy of biological processes. However, effective drug combination optimization requires the careful consideration of numerous parameters. The complexity of this optimization problem is clearly nontrivial and likely requires the assistance of advanced heuristic optimization techniques. In the current review, we discuss the application of optimization techniques for the identification of optimal drug combinations. More specifically, we focus on the application of phenotype-based screening approaches in the field of cancer therapy. These methods are divided into three categories: (1) modeling methods, (2) model-free approaches based on biological search algorithms, and (3) merged approaches, particularly phenotypically driven network biology methods and computation network models relying on phenotypic data. In addition to a brief description of each approach, we include a critical discussion of the advantages and disadvantages of each method, with a strong focus on the limitations and considerations needed to successfully apply such methods in biological research.