DYVIPAC: an integrated analysis and visualisation framework to probe multi-dimensional biological networks

The influence of circadian rhythms on CD8+ T cell activation upon vaccination: A mathematical modeling perspective

Circadian rhythms have been implicated in the modulation of many physiological processes, including those associated with the immune system. For example, these rhythms influence CD8+ T cell responses within the adaptive immune system. The mechanism underlying this immune-circadian interaction, however, remains unclear, particularly in the context of vaccination. Here, we devise a molecularly-explicit gene regulatory network model of early signaling in the naïve CD8+ T cell activation pathway, comprised of three axes (or subsystems) labeled ZAP70, LAT and CD28, to elucidate the molecular details of this immune-circadian mechanism and its relation to vaccination. This is done by coupling the model to a periodic forcing function to identify the molecular players targeted by circadian rhythms, and analyzing how these rhythms subsequently affect CD8+ T cell activation under differing levels of T cell receptor (TCR) phosphorylation, which we designate as vaccine load. By performing both bifurcation and parameter sensitivity analyses on the model at the single cell and ensemble levels, we find that applying periodic forcing on molecular targets within the ZAP70 axis is sufficient to create a day-night discrepancy in CD8+ T cell activation in a manner that is dependent on the bistable switch inherent in CD8+ T cell early signaling. We also demonstrate that the resulting CD8+ T cell activation is dependent on the strength of the periodic coupling as well as on the level of TCR phosphorylation. Our results show that this day-night discrepancy is not transmitted to certain downstream molecules within the LAT subsystem, such as mTORC1, suggesting a secondary, independent circadian regulation on that protein complex. We also corroborate experimental results by showing that the circadian regulation of CD8+ T cell primarily acts at a baseline, pre-vaccination state, playing a facilitating role in priming CD8+ T cells to vaccine inputs according to the time of day. By applying an ensemble level analysis using bifurcation theory and by including several hypothesized molecular targets of this circadian rhythm, we further demonstrate an increased variability between CD8+ T cells (due to heterogeneity) induced by its circadian regulation, which may allow an ensemble of CD8+ T cells to activate at a lower vaccine load, improving its sensitivity. This modeling study thus provides insights into the immune targets of the circadian clock, and proposes an interaction between vaccine load and the influence of circadian rhythms on CD8+ T cell activation.

Benchmarking tools for a priori identifiability analysis

MOTIVATION

The theoretical possibility of determining the state and parameters of a dynamic model by measuring its outputs is given by its structural identifiability and its observability. These properties should be analysed before attempting to calibrate a model, but their a priori analysis can be challenging, requiring symbolic calculations that often have a high computational cost. In recent years, a number of software tools have been developed for this task, mostly in the systems biology community. These tools have vastly different features and capabilities, and a critical assessment of their performance is still lacking.

RESULTS

Here, we present a comprehensive study of the computational resources available for analysing structural identifiability. We consider 13 software tools developed in 7 programming languages and evaluate their performance using a set of 25 case studies created from 21 models. Our results reveal their strengths and weaknesses, provide guidelines for choosing the most appropriate tool for a given problem and highlight opportunities for future developments.

AVAILABILITY AND IMPLEMENTATION

https://github.com/Xabo-RB/Benchmarking_files.

A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein-protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks. This combination was studied in the literature as a way to generate relaxation-type oscillations. Here, we show that the two feedbacks together ensure two types of oscillations, the relaxation-type ones and a smoother type of oscillations functioning in a very narrow range of frequencies, in such a way that outside that range, the amplitude of the oscillations is severely compromised. Even more, we show that the two feedbacks are essential for both oscillatory types to emerge, and it is their hierarchy what determines the type of oscillation at work. We used bifurcation analyses and amplitude vs. frequency curves to characterize and classify the oscillations. We also applied the same ideas to another simple model, with the goal of generalizing what we learned from signaling models. The results obtained display the wealth of oscillatory dynamics that exists in a system with a bistable module nested within a negative feedback loop, showing how to transition between different types of oscillations and other dynamical behaviors such as excitability. Our work provides a framework for the study of other oscillatory systems based on bistable modules, from simple two-component models to more complex examples like the MAPK cascade and experimental cases like cell cycle oscillators.

libRoadRunner 2.0: a high performance SBML simulation and analysis library

MOTIVATION

This article presents libRoadRunner 2.0, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models expressed using the systems biology markup language (SBML).

RESULTS

libRoadRunner is a self-contained library, able to run either as a component inside other tools via its C++, C and Python APIs, or interactively through its Python or Julia interface. libRoadRunner uses a custom just-in-time (JIT) compiler built on the widely used LLVM JIT compiler framework. It compiles SBML-specified models directly into native machine code for a large variety of processors, making it fast enough to simulate extremely large models or repeated runs in reasonable timeframes. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and non-linear algebraic equations) as well as several SBML extensions such as hierarchical composition and probability distributions. It offers multiple deterministic and stochastic integrators, as well as tools for steady-state, sensitivity, stability and structural analyses.

AVAILABILITY AND IMPLEMENTATION

libRoadRunner binary distributions for Windows, Mac OS and Linux, Julia and Python bindings, source code and documentation are all available at https://github.com/sys-bio/roadrunner, and Python bindings are also available via pip. The source code can be compiled for the supported systems as well as in principle any system supported by LLVM-13, such as ARM-based computers like the Raspberry Pi. The library is licensed under the Apache License Version 2.0.

Multi-Dimensional Analysis of Biochemical Network Dynamics Using pyDYVIPAC

Biochemical networks are dynamic, nonlinear, and high-dimensional systems. Realistic kinetic models of biochemical networks often comprise a multitude of kinetic parameters and state variables. Depending on the specific parameter values, a network can display one of a variety of possible dynamic behaviors such as monostable fixed point, damped oscillation, sustained oscillation, and/or bistability. Understanding how a network behaves under a particular parametric condition, and how its behavior changes as the model parameters are varied within the multidimensional parameter space are imperative for gaining a holistic understanding of the network dynamics. Such knowledge helps elucidate the parameter-to-dynamics mapping, uncover how cells make decisions under various pathophysiological contexts, and inform the design of biological circuits with desired behavior, where the latter is critical to the field of synthetic biology. In this chapter, we will present a practical guide to the multidimensional exploration, analysis, and visualization of network dynamics using pyDYVIPAC, which is a tool ideally suited to these purposes implemented in Python. The utility of pyDYVIPAC will be demonstrated using specific examples of biochemical networks with differing structures and dynamic properties via the interactive Jupyter Notebook environment.

Bayesian parameter estimation for dynamical models in systems biology

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.

Interactive Data Visualization Tool for Patient-Centered Decision Making in Kidney Cancer

PURPOSE

Patients and providers often lack clinical decision tools to enable effective shared decision making. This is especially true in the rapidly changing therapeutic landscape of metastatic kidney cancer. Using the International Metastatic Renal Cell Carcinoma Database Consortium (IMDC) criteria, a validated risk prediction tool for patients with metastatic renal cell carcinoma, we created and user-tested a novel interactive visualization for clinical use.

METHODS

An interactive visualization depicting IMDC criteria was created, with the final version including data for more than 4,500 patients. Usability testing was performed with nonmedical lay-users and medical oncology fellow physicians. Subjects used the tool to calculate median survival times based on IMDC criteria. User confidence was surveyed. An iterative user feedback implementation cycle was completed and informed revision of the tool.

RESULTS

The tool is available at CloViz-IMDC. Initially, 400 lay-users and 15 physicians completed clinical scenarios and surveys. Cumulative accuracy across scenarios was higher for physicians than lay-users (84% v 74%; P = .03). Eighty-three percent of lay-users and 87% of physicians thought the tool became intuitive with use. Sixty-eight percent of lay-users wanted to use the tool clinically compared with 87% of physicians. After revisions, the updated tool was user-tested with 100 lay-users and 15 physicians. Physicians, but not lay-users, showed significant improvement in accuracy in the updated version of the tool (90% v 67%; P = .008). Seventy-two percent of lay-users and 93% of physicians wanted to use the updated tool in a clinical setting.

CONCLUSION

A graphical method of interacting with a validated nomogram provides prognosis results that can be used by nonmedical lay-users and physicians, and has the potential for expanded use across many clinical conditions.

Molecular noise filtering in the β-adrenergic signaling network by phospholamban pentamers

Phospholamban (PLN) is an important regulator of cardiac calcium handling due to its ability to inhibit the calcium ATPase SERCA. β-Adrenergic stimulation reverses SERCA inhibition via PLN phosphorylation and facilitates fast calcium reuptake. PLN also forms pentamers whose physiological significance has remained elusive. Using mathematical modeling combined with biochemical and cell biological experiments, we show that pentamers regulate both the dynamics and steady-state levels of monomer phosphorylation. Substrate competition by pentamers and a feed-forward loop involving inhibitor-1 can delay monomer phosphorylation by protein kinase A (PKA), whereas cooperative pentamer dephosphorylation enables bistable PLN steady-state phosphorylation. Simulations show that phosphorylation delay and bistability act as complementary filters that reduce the effect of random fluctuations in PKA activity, thereby ensuring consistent monomer phosphorylation and SERCA activity despite noisy upstream signals. Preliminary analyses suggest that the PLN mutation R14del could impair noise filtering, offering a new perspective on how this mutation causes cardiac arrhythmias.

Modeling the Nonlinear Dynamics of Intracellular Signaling Networks

This protocol illustrates a pipeline for modeling the nonlinear behavior of intracellular signaling pathways. At fixed spatial points, nonlinear signaling dynamics are described by ordinary differential equations (ODEs). At constant parameters, these ODEs may have multiple attractors, such as multiple steady states or limit cycles. Standard optimization procedures fine-tune the parameters for the system trajectories localized within the basin of attraction of only one attractor, usually a stable steady state. The suggested protocol samples the parameter space and captures the overall dynamic behavior by analyzing the number and stability of steady states and the shapes of the assembly of nullclines, which are determined as projections of quasi-steady-state trajectories into different 2D spaces of system variables. Our pipeline allows identifying main qualitative features of the model behavior, perform bifurcation analysis, and determine the borders separating the different dynamical regimes within the assembly of 2D parametric planes. Partial differential equation (PDE) systems describing the nonlinear spatiotemporal behavior are derived by coupling fixed point dynamics with species diffusion.

Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration

Migrating cells need to coordinate distinct leading and trailing edge dynamics but the underlying mechanisms are unclear. Here, we combine experiments and mathematical modeling to elaborate the minimal autonomous biochemical machinery necessary and sufficient for this dynamic coordination and cell movement. RhoA activates Rac1 via DIA and inhibits Rac1 via ROCK, while Rac1 inhibits RhoA through PAK. Our data suggest that in motile, polarized cells, RhoA–ROCK interactions prevail at the rear, whereas RhoA-DIA interactions dominate at the front where Rac1/Rho oscillations drive protrusions and retractions. At the rear, high RhoA and low Rac1 activities are maintained until a wave of oscillatory GTPase activities from the cell front reaches the rear, inducing transient GTPase oscillations and RhoA activity spikes. After the rear retracts, the initial GTPase pattern resumes. Our findings show how periodic, propagating GTPase waves coordinate distinct GTPase patterns at the leading and trailing edge dynamics in moving cells.

Exploratory Data Analysis of Adverse Birth Outcomes and Exposure to Oxides of Nitrogen Using Interactive Parallel Coordinates Plot Technique

We propose that a parallel coordinates plot can be used to study multidimensional data particularly to explore discovery of patterns across the variables. This can assist researchers from the health sciences to visualize their cohort data with interactive data analysis. The study used data from Mother and Child in the Environment birth cohort in Durban, South Africa for the period 2013 to 2017 retrospectively registered. In this paper, we demonstrate that the exploration of multidimensional data with parallel coordinates plot and use of brushing using different colours assists with the identification of relationships and patterns. Parallel coordinates plot visualization facilitates the researcher's skills to find trends, identify outliers and perform quality checks in large multivariate data. We have identified trends in the data that provide directions for further research, and illustrated thereby the potential of parallel coordinates plot to explore patterns and relationships of prenatal oxides of nitrogen exposure with multidimensional birth outcomes. The study recognized the co-occurrence of adverse birth outcomes among infants and these infants had mothers with moderate to high level of NOx exposure during pregnancy. Brushing using different colours facilitated the detection of patterns of relationships to perform basic and advanced statistical model-based analysis.

Simple Rho GTPase Dynamics Generate a Complex Regulatory Landscape Associated with Cell Shape

Migratory cells exhibit a variety of morphologically distinct responses to their environments that manifest in their cell shape. Some protrude uniformly to increase substrate contacts, others are broadly contractile, some polarize to facilitate migration, and yet others exhibit mixtures of these responses. Prior studies have identified a discrete collection of shapes that the majority of cells display and demonstrated that activity levels of the cytoskeletal regulators Rac1 and RhoA GTPase regulate those shapes. Here, we use computational modeling to assess whether known GTPase dynamics can give rise to a sufficient diversity of spatial signaling states to explain the observed shapes. Results show that the combination of autoactivation and mutually antagonistic cross talk between GTPases, along with the conservative membrane binding, generates a wide array of distinct homogeneous and polarized regulatory phenotypes that arise for fixed model parameters. From a theoretical perspective, these results demonstrate that simple GTPase dynamics can generate complex multistability in which six distinct stable steady states (three homogeneous and three polarized) coexist for a fixed set of parameters, each of which naturally maps to an observed morphology. From a biological perspective, although we do not explicitly model the cytoskeleton or resulting cell morphologies, these results, along with prior literature linking GTPase activity to cell morphology, support the hypothesis that GTPase signaling dynamics can generate the broad morphological characteristics observed in many migratory cell populations. Further, the observed diversity may be the result of cells populating a complex morphological landscape generated by GTPase regulation rather than being the result of intrinsic cell-cell variation. These results demonstrate that Rho GTPases may have a central role in regulating the broad characteristics of cell shape (e.g., expansive, contractile, polarized, etc.) and that shape heterogeneity may be (at least partly) a reflection of the rich signaling dynamics regulating the cytoskeleton rather than intrinsic cell heterogeneity.

Human Papillomavirus Early Promoter Regulatory Core as a Bistable Switch

High risk human papillomavirus (HPV) can induce cervical and oropharyngeal cancerous lesions. Different HPV strains, as well as still unknown mechanisms can be associated to a range of biochemical parameters that can importantly affect the HPV gene expression dynamics. For this reason, it is of pivotal importance to investigate how parameters variation can induce interesting behaviors such as viral latency in place of the normal gene replication activity. The aim of this study is to perform bifurcation analysis on a minimal model of the early promoter regulatory core controlled by E2 transcriptional regulation. The bifurcation analysis showed how E2 regulation can induce a bistability on the early promoter gene expression that could explain the interplay between viral latency and gene replication regimen.

Uncovering Bistability in the Rac1/RhoA Signaling Network Through Integrating Computational Modeling and Experimentation

The members of the Rho family of small guanosine triphosphatases (GTPases), Rac1 and RhoA, play critical roles in the regulation of cell migration, actin dynamics, and cytoskeletal system. It has been long known that a mutual inhibition relationship exists between Rac1 and RhoA, and the Rac1/RhoA circuitry has been theoretically predicted to be capable of displaying bistability, a phenomenon whereby a system could settle in either one of the two stable steady states. However, it was only until recently that bistable behavior was demonstrated experimentally both at the biochemical and cellular phenotypic levels, through an integrative approach combining computational modeling and wet-lab experimentation. Here, we describe how such systems biology approaches could be employed to uncover bistability and its hallmark features, using the Rac1/RhoA network as an illustrative example. This may provide guidance for future work aimed at identifying bistable behaviors in other cellular processes.

Dynamic modelling of the mTOR signalling network reveals complex emergent behaviours conferred by DEPTOR

The mechanistic Target of Rapamycin (mTOR) signalling network is an evolutionarily conserved network that controls key cellular processes, including cell growth and metabolism. Consisting of the major kinase complexes mTOR Complex 1 and 2 (mTORC1/2), the mTOR network harbours complex interactions and feedback loops. The DEP domain-containing mTOR-interacting protein (DEPTOR) was recently identified as an endogenous inhibitor of both mTORC1 and 2 through direct interactions, and is in turn degraded by mTORC1/2, adding an extra layer of complexity to the mTOR network. Yet, the dynamic properties of the DEPTOR-mTOR network and the roles of DEPTOR in coordinating mTORC1/2 activation dynamics have not been characterised. Using computational modelling, systems analysis and dynamic simulations we show that DEPTOR confers remarkably rich and complex dynamic behaviours to mTOR signalling, including abrupt, bistable switches, oscillations and co-existing bistable/oscillatory responses. Transitions between these distinct modes of behaviour are enabled by modulating DEPTOR expression alone. We characterise the governing conditions for the observed dynamics by elucidating the network in its vast multi-dimensional parameter space, and develop strategies to identify core network design motifs underlying these dynamics. Our findings provide new systems-level insights into the complexity of mTOR signalling contributed by DEPTOR.

Exploring and visualizing multidimensional data in translational research platforms

The unprecedented advances in technology and scientific research over the past few years have provided the scientific community with new and more complex forms of data. Large data sets collected from single groups or cross-institution consortiums containing hundreds of omic and clinical variables corresponding to thousands of patients are becoming increasingly commonplace in the research setting. Before any core analyses are performed, visualization often plays a key role in the initial phases of research, especially for projects where no initial hypotheses are dominant. Proper visualization of data at a high level facilitates researcher's abilities to find trends, identify outliers and perform quality checks. In addition, research has uncovered the important role of visualization in data analysis and its implied benefits facilitating our understanding of disease and ultimately improving patient care. In this work, we present a review of the current landscape of existing tools designed to facilitate the visualization of multidimensional data in translational research platforms. Specifically, we reviewed the biomedical literature for translational platforms allowing the visualization and exploration of clinical and omics data, and identified 11 platforms: cBioPortal, interactive genomics patient stratification explorer, Igloo-Plot, The Georgetown Database of Cancer Plus, tranSMART, an unnamed data-cube-based model supporting heterogeneous data, Papilio, Caleydo Domino, Qlucore Omics, Oracle Health Sciences Translational Research Center and OmicsOffice® powered by TIBCO Spotfire. In a health sector continuously witnessing an increase in data from multifarious sources, visualization tools used to better grasp these data will grow in their importance, and we believe our work will be useful in guiding investigators in similar situations.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.

Structural Identifiability of Dynamic Systems Biology Models

A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areas.

Bistability in the Rac1, PAK, and RhoA Signaling Network Drives Actin Cytoskeleton Dynamics and Cell Motility Switches

Dynamic interactions between RhoA and Rac1, members of the Rho small GTPase family, play a vital role in the control of cell migration. Using predictive mathematical modeling, mass spectrometry-based quantitation of network components, and experimental validation in MDA-MB-231 mesenchymal breast cancer cells, we show that a network containing Rac1, RhoA, and PAK family kinases can produce bistable, switch-like responses to a graded PAK inhibition. Using a small chemical inhibitor of PAK, we demonstrate that cellular RhoA and Rac1 activation levels respond in a history-dependent, bistable manner to PAK inhibition. Consequently, we show that downstream signaling, actin dynamics, and cell migration also behave in a bistable fashion, displaying switches and hysteresis in response to PAK inhibition. Our results demonstrate that PAK is a critical component in the Rac1-RhoA inhibitory crosstalk that governs bistable GTPase activity, cell morphology, and cell migration switches.

•

RhoA and Rac1 are linked by a double-negative feedback loop

•

A model predicts bistability of the system within a physiological parameter range

•

Rac1 and RhoA activity is bistable in response to PAK inhibition

•

Actin dynamics, cell morphology, and migration show hysteresis upon PAK inhibition

Flipping the Rac-Rho Switch in Cell Motility

Mutual inhibition of Rac and Rho GTPases leads to bistability and hysteresis at both the biochemical and cell behavior levels.