Robustness portraits of diverse biological networks conserved despite order-of-magnitude parameter uncertainty

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.

Slow Delayed Rectifier Current Protects Ventricular Myocytes From Arrhythmic Dynamics Across Multiple Species: A Computational Study

BACKGROUND

The slow and rapid delayed rectifier K⁺ currents (I_Ks and I_Kr, respectively) are responsible for repolarizing the ventricular action potential (AP) and preventing abnormally long APs that may lead to arrhythmias. Although differences in biophysical properties of the 2 currents have been carefully documented, the respective physiological roles of I_Kr and I_Ks are less established. In this study, we sought to understand the individual roles of these currents and quantify how effectively each stabilizes the AP and protects cells against arrhythmias across multiple species.

METHODS

We compared 10 mathematical models describing ventricular myocytes from human, rabbit, dog, and guinea pig. We examined variability within heterogeneous cell populations, tested the susceptibility of cells to proarrhythmic behavior, and studied how I_Ks and I_Kr responded to changes in the AP.

RESULTS

We found that (1) models with higher baseline I_Ks exhibited less cell-to-cell variability in AP duration; (2) models with higher baseline I_Ks were less susceptible to early afterdepolarizations induced by depolarizing perturbations; (3) as AP duration is lengthened, I_Ks increases more profoundly than I_Kr, thereby providing negative feedback that resists excessive AP prolongation; and (4) the increase in I_Ks that occurs during β-adrenergic stimulation is critical for protecting cardiac myocytes from early afterdepolarizations under these conditions.

CONCLUSIONS

Slow delayed rectifier current is uniformly protective across a variety of cell types. These results suggest that I_Ks enhancement could potentially be an effective antiarrhythmic strategy.

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.

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.

An engineering design approach to systems biology

Measuring and modeling the integrated behavior of biomolecular-cellular networks is central to systems biology. Over several decades, systems biology has been shaped by quantitative biologists, physicists, mathematicians, and engineers in different ways. However, the basic and applied versions of systems biology are not typically distinguished, which blurs the separate aspirations of the field and its potential for real-world impact. Here, we articulate an engineering approach to systems biology, which applies educational philosophy, engineering design, and predictive models to solve contemporary problems in an age of biomedical Big Data. A concerted effort to train systems bioengineers will provide a versatile workforce capable of tackling the diverse challenges faced by the biotechnological and pharmaceutical sectors in a modern, information-dense economy.

Comprehensive analyses of ventricular myocyte models identify targets exhibiting favorable rate dependence

Reverse rate dependence is a problematic property of antiarrhythmic drugs that prolong the cardiac action potential (AP). The prolongation caused by reverse rate dependent agents is greater at slow heart rates, resulting in both reduced arrhythmia suppression at fast rates and increased arrhythmia risk at slow rates. The opposite property, forward rate dependence, would theoretically overcome these parallel problems, yet forward rate dependent (FRD) antiarrhythmics remain elusive. Moreover, there is evidence that reverse rate dependence is an intrinsic property of perturbations to the AP. We have addressed the possibility of forward rate dependence by performing a comprehensive analysis of 13 ventricular myocyte models. By simulating populations of myocytes with varying properties and analyzing population results statistically, we simultaneously predicted the rate-dependent effects of changes in multiple model parameters. An average of 40 parameters were tested in each model, and effects on AP duration were assessed at slow (0.2 Hz) and fast (2 Hz) rates. The analysis identified a variety of FRD ionic current perturbations and generated specific predictions regarding their mechanisms. For instance, an increase in L-type calcium current is FRD when this is accompanied by indirect, rate-dependent changes in slow delayed rectifier potassium current. A comparison of predictions across models identified inward rectifier potassium current and the sodium-potassium pump as the two targets most likely to produce FRD AP prolongation. Finally, a statistical analysis of results from the 13 models demonstrated that models displaying minimal rate-dependent changes in AP shape have little capacity for FRD perturbations, whereas models with large shape changes have considerable FRD potential. This can explain differences between species and between ventricular cell types. Overall, this study provides new insights, both specific and general, into the determinants of AP duration rate dependence, and illustrates a strategy for the design of potentially beneficial antiarrhythmic drugs.

Several drugs intended to treat cardiac arrhythmias have failed because of unfavorable rate-dependent properties. That is, the drugs fail to alter electrical activity at fast heart rates, where this would be beneficial, but they do affect electrical activity at slow rates, where this is unwanted. In targeted studies, several agents have been shown to exhibit these unfavorable properties, suggesting that these rate-dependent responses may be intrinsic to ventricular muscle. To determine whether drugs with desirable rate-dependent properties could be rationally designed, we performed comprehensive and systematic analyses of several heart cell models. These analyses calculated the rate-dependent properties of changes in any model parameter, thereby generating simultaneously a large number of model predictions. The analyses showed that targets with favorable rate-dependent properties could indeed be identified, and further simulations uncovered the mechanisms underlying these behaviors. Moreover, a quantitative comparison of results obtained in different models provided new insight in why a given drug applied to different species, or to different tissue types, might produce different rate-dependent behaviors. Overall this study shows how a comprehensive and systematic approach to heart cell models can both identify novel targets and produce more general insight into rate-dependent alterations to cardiac electrical activity.

A compartmentalized mathematical model of the β1-adrenergic signaling system in mouse ventricular myocytes

The β₁-adrenergic signaling system plays an important role in the functioning of cardiac cells. Experimental data shows that the activation of this system produces inotropy, lusitropy, and chronotropy in the heart, such as increased magnitude and relaxation rates of [Ca²⁺]_i transients and contraction force, and increased heart rhythm. However, excessive stimulation of β₁-adrenergic receptors leads to heart dysfunction and heart failure. In this paper, a comprehensive, experimentally based mathematical model of the β₁-adrenergic signaling system for mouse ventricular myocytes is developed, which includes major subcellular functional compartments (caveolae, extracaveolae, and cytosol). The model describes biochemical reactions that occur during stimulation of β₁-adrenoceptors, changes in ionic currents, and modifications of Ca²⁺ handling system. Simulations describe the dynamics of major signaling molecules, such as cyclic AMP and protein kinase A, in different subcellular compartments; the effects of inhibition of phosphodiesterases on cAMP production; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca²⁺ handling proteins; modifications of action potential shape and duration; magnitudes and relaxation rates of [Ca²⁺]_i transients; changes in intracellular and transmembrane Ca²⁺ fluxes; and [Na⁺]_i fluxes and dynamics. The model elucidates complex interactions of ionic currents upon activation of β₁-adrenoceptors at different stimulation frequencies, which ultimately lead to a relatively modest increase in action potential duration and significant increase in [Ca²⁺]_i transients. In particular, the model includes two subpopulations of the L-type Ca²⁺ channels, in caveolae and extracaveolae compartments, and their effects on the action potential and [Ca²⁺]_i transients are investigated. The presented model can be used by researchers for the interpretation of experimental data and for the developments of mathematical models for other species or for pathological conditions.

Integrating fluorescent biosensor data using computational models

This book chapter provides a tutorial on how to construct computational models of signaling networks for the integration and interpretation of FRET-based biosensor data. A model of cAMP production and PKA activation is presented to provide an example of the model building process. The computational model is defined using hypothesized signaling network structure and measured kinetic parameters and then simulated in Virtual Cell software. Experimental acquisition and processing of FRET biosensor data is discussed in the context of model validation. This data is then used to fit parameters of the computational model such that the model can more accurately predict experimental data. Finally, this model is used to show how computational experiments can interrogate signaling networks and provide testable hypotheses. This simple, yet detailed, tutorial on how to use computational models provides biologists that use biosensors a powerful tool to further probe and evaluate the underpinnings of a biological response.

Robustness of signal transduction pathways

Signal transduction pathways transduce information about the outside of the cell to the nucleus, regulating gene expression and cell fate. To reliably inform the cell about its surroundings, information transfer has to be robust against typical perturbation that a cell experiences. Robustness of several mammalian signaling pathways has been studied recently by quantitative experimentation and using mathematical modeling. Here, we review these studies, and describe the emerging concepts of robustness and the underlying mechanisms.

Multiscale models of cell signaling

Computational models of signal transduction face challenges of scale below the resolution of a single cell. Here, we organize these challenges around three key interfaces for multiscale models of cell signaling: molecules to pathways, pathways to networks, and networks to outcomes. Each interface requires its own set of computational approaches and systems-level data, and no single approach or dataset can effectively bridge all three interfaces. This suggests that realistic "whole-cell" models of signaling will need to agglomerate different model types that span critical intracellular scales. Future multiscale models will be valuable for understanding the impact of signaling mutations or population variants that lead to cellular diseases such as cancer.