Workflow for generating competing hypothesis from models with parameter uncertainty

Computationally Modelling Cholesterol Metabolism and Atherosclerosis

Cardiovascular disease (CVD) is the leading cause of death globally. The underlying pathological driver of CVD is atherosclerosis. The primary risk factor for atherosclerosis is elevated low-density lipoprotein cholesterol (LDL-C). Dysregulation of cholesterol metabolism is synonymous with a rise in LDL-C. Due to the complexity of cholesterol metabolism and atherosclerosis mathematical models are routinely used to explore their non-trivial dynamics. Mathematical modelling has generated a wealth of useful biological insights, which have deepened our understanding of these processes. To date however, no model has been developed which fully captures how whole-body cholesterol metabolism intersects with atherosclerosis. The main reason for this is one of scale. Whole body cholesterol metabolism is defined by macroscale physiological processes, while atherosclerosis operates mainly at a microscale. This work describes how a model of cholesterol metabolism was combined with a model of atherosclerotic plaque formation. This new model is capable of reproducing the output from its parent models. Using the new model, we demonstrate how this system can be utilized to identify interventions that lower LDL-C and abrogate plaque formation.

In silico model of atherosclerosis with individual patient calibration to enable precision medicine for cardiovascular disease

OBJECTIVE

Guidance for preventing myocardial infarction and ischemic stroke by tailoring treatment for individual patients with atherosclerosis is an unmet need. Such development may be possible with computational modeling. Given the multifactorial biology of atherosclerosis, modeling must be based on complete biological networks that capture protein-protein interactions estimated to drive disease progression. Here, we aimed to develop a clinically relevant scale model of atherosclerosis, calibrate it with individual patient data, and use it to simulate optimized pharmacotherapy for individual patients.

APPROACH AND RESULTS

The study used a uniquely constituted plaque proteomic dataset to create a comprehensive systems biology disease model for simulating individualized responses to pharmacotherapy. Plaque tissue was collected from 18 patients with 6735 proteins at two locations per patient. 113 pathways were identified and included in the systems biology model of endothelial cells, vascular smooth muscle cells, macrophages, lymphocytes, and the integrated intima, altogether spanning 4411 proteins, demonstrating a range of 39-96% plaque instability. After calibrating the systems biology models for individual patients, we simulated intensive lipid-lowering, anti-inflammatory, and anti-diabetic drugs. We also simulated a combination therapy. Drug response was evaluated as the degree of change in plaque stability, where an improvement was defined as a reduction of plaque instability. In patients with initially unstable lesions, simulated responses varied from high (20%, on combination therapy) to marginal improvement, whereas patients with initially stable plaques showed generally less improvement.

CONCLUSION

In this pilot study, proteomics-based system biology modeling was shown to simulate drug response based on atherosclerotic plaque instability with a power of 90%, providing a potential strategy for improved personalized management of patients with cardiovascular disease.

Modeling cholesterol metabolism and atherosclerosis

Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.

Virtual Transcriptomics: Noninvasive Phenotyping of Atherosclerosis by Decoding Plaque Biology From Computed Tomography Angiography Imaging

[Figure: see text].

Cholesterol Homeostasis: An In Silico Investigation into How Aging Disrupts Its Key Hepatic Regulatory Mechanisms

The dysregulation of intracellular cholesterol homeostasis is associated with several age-related diseases, most notably cardiovascular disease (CVD). Research in this area has benefitted from using computational modelling to study the inherent complexity associated with the regulation of this system. In addition to facilitating hypothesis exploration, the utility of modelling lies in its ability to represent an array of rate limiting enzymatic reactions, together with multiple feedback loops, which collectively define the dynamics of cholesterol homeostasis. However, to date no model has specifically investigated the effects aging has on this system. This work addresses this shortcoming by explicitly focusing on the impact of aging on hepatic intracellular cholesterol homeostasis. The model was used to investigate the experimental findings that reactive oxygen species induce the total activation of 3-hydroxy-3-methylglutaryl-coenzyme A (HMG-CoA) reductase (HMGCR). Moreover, the model explored the impact of an age-related decrease in hepatic acetyl-CoA acetyltransferase 2 (ACAT2). The model suggested that an increase in the activity of HMGCR does not have as significant an impact on cholesterol homeostasis as a decrease in hepatic ACAT2 activity. According to the model, a decrease in the activity of hepatic ACAT2 raises free cholesterol (FC) and decreases low-density lipoprotein cholesterol (LDL-C) levels. Increased acetyl CoA synthesis resulted in a reduction in the number of hepatic low-density lipoprotein receptors, and increased LDL-C, FC, and cholesterol esters. The rise in LDL-C was restricted by elevated hepatic FC accumulation. Taken together these findings have important implications for healthspan. This is because emerging clinical data suggest hepatic FC accumulation is relevant to the pathogenesis of non-alcoholic fatty liver disease (NAFLD), which is associated with an increased risk of CVD. These pathophysiological changes could, in part, help to explain the phenomenon of increased mortality associated with low levels of LDL-C which have been observed in certain studies involving the oldest old (≥85 years).

Uncertainty quantification, propagation and characterization by Bayesian analysis combined with global sensitivity analysis applied to dynamical intracellular pathway models

Motivation

Dynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis (GSA) in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as to give guidance on parameters that are essential in distinguishing different qualitative output behaviours.

Results

We used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a GSA was performed on the predictions using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions. This approach is useful both for experimental design as well as model building.

Availability and implementation

Source code is freely available at https://github.com/alexjau/uqsa.

Supplementary information

Supplementary data are available at Bioinformatics online.

New models of atherosclerosis and multi-drug therapeutic interventions

Motivation

Atherosclerosis is amongst the leading causes of death globally. However, it is challenging to study in vivo or in vitro and no detailed, openly-available computational models exist. Clinical studies hint that pharmaceutical therapy may be possible. Here, we develop the first detailed, computational model of atherosclerosis and use it to develop multi-drug therapeutic hypotheses.

Results

We assembled a network describing atheroma development from the literature. Maps and mathematical models were produced using the Systems Biology Graphical Notation and Systems Biology Markup Language, respectively. The model was constrained against clinical and laboratory data. We identified five drugs that together potentially reverse advanced atheroma formation.

Availability and implementation

The map is available in the Supplementary Material in SBGN-ML format. The model is available in the Supplementary Material and from BioModels, a repository of SBML models, containing CellDesigner markup.

Supplementary information

Supplementary data are available at Bioinformatics online.

A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference

Systems in nature capable of collective behaviour are nonlinear, operating across several scales. Yet our ability to account for their collective dynamics differs in physics, chemistry and biology. Here, we briefly review the similarities and differences between mathematical modelling of adaptive living systems versus physico-chemical systems. We find that physics-based chemistry modelling and computational neuroscience have a shared interest in developing techniques for model reductions aiming at the identification of a reduced subsystem or slow manifold, capturing the effective dynamics. By contrast, as relations and kinetics between biological molecules are less characterized, current quantitative analysis under the umbrella of bioinformatics focuses on signal extraction, correlation, regression and machine-learning analysis. We argue that model reduction analysis and the ensuing identification of manifolds bridges physics and biology. Furthermore, modelling living systems presents deep challenges as how to reconcile rich molecular data with inherent modelling uncertainties (formalism, variables selection and model parameters). We anticipate a new generative data-driven modelling paradigm constrained by identified governing principles extracted from low-dimensional manifold analysis. The rise of a new generation of models will ultimately connect biology to quantitative mechanistic descriptions, thereby setting the stage for investigating the character of the model language and principles driving living systems.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

A Six-Stage Workflow for Robust Application of Systems Pharmacology

Quantitative and systems pharmacology (QSP) is increasingly being applied in pharmaceutical research and development. One factor critical to the ultimate success of QSP is the establishment of commonly accepted language, technical criteria, and workflows. We propose an integrated workflow that bridges conceptual objectives with underlying technical detail to support the execution, communication, and evaluation of QSP projects.

Multilevel functional genomics data integration as a tool for understanding physiology: a network biology perspective

The overall aim of physiological research is to understand how living systems function in an integrative manner. Consequently, the discipline of physiology has since its infancy attempted to link multiple levels of biological organization. Increasingly this has involved mathematical and computational approaches, typically to model a small number of components spanning several levels of biological organization. With the advent of “omics” technologies, which can characterize the molecular state of a cell or tissue (intended as the level of expression and/or activity of its molecular components), the number of molecular components we can quantify has increased exponentially. Paradoxically, the unprecedented amount of experimental data has made it more difficult to derive conceptual models underlying essential mechanisms regulating mammalian physiology. We present an overview of state-of-the-art methods currently used to identifying biological networks underlying genomewide responses. These are based on a data-driven approach that relies on advanced computational methods designed to “learn” biology from observational data. In this review, we illustrate an application of these computational methodologies using a case study integrating an in vivo model representing the transcriptional state of hypoxic skeletal muscle with a clinical study representing muscle wasting in chronic obstructive pulmonary disease patients. The broader application of these approaches to modeling multiple levels of biological data in the context of modern physiology is discussed.

Signaling networks in MS: a systems-based approach to developing new pharmacological therapies

The pathogenesis of multiple sclerosis (MS) involves alterations to multiple pathways and processes, which represent a significant challenge for developing more-effective therapies. Systems biology approaches that study pathway dysregulation should offer benefits by integrating molecular networks and dynamic models with current biological knowledge for understanding disease heterogeneity and response to therapy. In MS, abnormalities have been identified in several cytokine-signaling pathways, as well as those of other immune receptors. Among the downstream molecules implicated are Jak/Stat, NF-Kb, ERK1/3, p38 or Jun/Fos. Together, these data suggest that MS is likely to be associated with abnormalities in apoptosis/cell death, microglia activation, blood-brain barrier functioning, immune responses, cytokine production, and/or oxidative stress, although which pathways contribute to the cascade of damage and can be modulated remains an open question. While current MS drugs target some of these pathways, others remain untouched. Here, we propose a pragmatic systems analysis approach that involves the large-scale extraction of processes and pathways relevant to MS. These data serve as a scaffold on which computational modeling can be performed to identify disease subgroups based on the contribution of different processes. Such an analysis, targeting these relevant MS-signaling pathways, offers the opportunity to accelerate the development of novel individual or combination therapies.

Physiologically realistic and validated mathematical liver model reveals [corrected] hepatobiliary transfer rates for Gd-EOB-DTPA using human DCE-MRI data

Objectives

Diffuse liver disease (DLD), such as non-alcoholic fatty liver disease (NASH) and cirrhosis, is a rapidly growing problem throughout the Westernized world. Magnetic resonance imaging (MRI), based on uptake of the hepatocyte-specific contrast agent (CA) Gd-EOB-DTPA, is a promising non-invasive approach for diagnosing DLD. However, to fully utilize the potential of such dynamic measurements for clinical or research purposes, more advanced methods for data analysis are required.

Methods

A mathematical model that can be used for such data-analysis was developed. Data was obtained from healthy human subjects using a clinical protocol with high spatial resolution. The model is based on ordinary differential equations and goes beyond local diffusion modeling, taking into account the complete system accessible to the CA.

Results

The presented model can describe the data accurately, which was confirmed using chi-square statistics. Furthermore, the model is minimal and identifiable, meaning that all parameters were determined with small degree of uncertainty. The model was also validated using independent data.

Conclusions

We have developed a novel approach for determining previously undescribed physiological hepatic parameters in humans, associated with CA transport across the liver. The method has a potential for assessing regional liver function in clinical examinations of patients that are suffering of DLD and compromised hepatic function.

The common ground of genomics and systems biology

The rise of systems biology is intertwined with that of genomics, yet their primordial relationship to one another is ill-defined. We discuss how the growth of genomics provided a critical boost to the popularity of systems biology. We describe the parts of genomics that share common areas of interest with systems biology today in the areas of gene expression, network inference, chromatin state analysis, pathway analysis, personalized medicine, and upcoming areas of synergy as genomics continues to expand its scope across all biomedical fields.

Parameter trajectory analysis to identify treatment effects of pharmacological interventions

The field of medical systems biology aims to advance understanding of molecular mechanisms that drive disease progression and to translate this knowledge into therapies to effectively treat diseases. A challenging task is the investigation of long-term effects of a (pharmacological) treatment, to establish its applicability and to identify potential side effects. We present a new modeling approach, called Analysis of Dynamic Adaptations in Parameter Trajectories (ADAPT), to analyze the long-term effects of a pharmacological intervention. A concept of time-dependent evolution of model parameters is introduced to study the dynamics of molecular adaptations. The progression of these adaptations is predicted by identifying necessary dynamic changes in the model parameters to describe the transition between experimental data obtained during different stages of the treatment. The trajectories provide insight in the affected underlying biological systems and identify the molecular events that should be studied in more detail to unravel the mechanistic basis of treatment outcome. Modulating effects caused by interactions with the proteome and transcriptome levels, which are often less well understood, can be captured by the time-dependent descriptions of the parameters. ADAPT was employed to identify metabolic adaptations induced upon pharmacological activation of the liver X receptor (LXR), a potential drug target to treat or prevent atherosclerosis. The trajectories were investigated to study the cascade of adaptations. This provided a counter-intuitive insight concerning the function of scavenger receptor class B1 (SR-B1), a receptor that facilitates the hepatic uptake of cholesterol. Although activation of LXR promotes cholesterol efflux and -excretion, our computational analysis showed that the hepatic capacity to clear cholesterol was reduced upon prolonged treatment. This prediction was confirmed experimentally by immunoblotting measurements of SR-B1 in hepatic membranes. Next to the identification of potential unwanted side effects, we demonstrate how ADAPT can be used to design new target interventions to prevent these.

A driving ambition of medical systems biology is to advance our understanding of molecular processes that drive the progression of complex diseases such as Type 2 Diabetes and cardiovascular disease. This insight is essential to enable the development of therapies to effectively treat diseases. A challenging task is to investigate the long-term effects of a treatment, in order to establish its applicability and to identify potential side effects. As such, there is a growing need for novel approaches to support this research. Here, we present a new computational approach to identify treatment effects. We make use of a computational model of the biological system. The model is used to describe the experimental data obtained during different stages of the treatment. To incorporate the long-term/progressive adaptations in the system, induced by changes in gene and protein expression, the model is iteratively updated. The approach was employed to identify metabolic adaptations induced by a potential anti-atherosclerotic and anti-diabetic drug target. Our approach identifies the molecular events that should be studied in more detail to establish the mechanistic basis of treatment outcome. New biological insight was obtained concerning the metabolism of cholesterol, which was in turn experimentally validated.

Parameter uncertainty in biochemical models described by ordinary differential equations

Improved mechanistic understanding of biochemical networks is one of the driving ambitions of Systems Biology. Computational modeling allows the integration of various sources of experimental data in order to put this conceptual understanding to the test in a quantitative manner. The aim of computational modeling is to obtain both predictive as well as explanatory models for complex phenomena, hereby providing useful approximations of reality with varying levels of detail. As the complexity required to describe different system increases, so does the need for determining how well such predictions can be made. Despite efforts to make tools for uncertainty analysis available to the field, these methods have not yet found widespread use in the field of Systems Biology. Additionally, the suitability of the different methods strongly depends on the problem and system under investigation. This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.

Conclusions via unique predictions obtained despite unidentifiability--new definitions and a general method

It is often predicted that model-based data analysis will revolutionize biology, just as it has physics and engineering. A widely used tool within such analysis is hypothesis testing, which focuses on model rejections. However, the fact that a systems biology model is non-rejected is often a relatively weak statement, as such models usually are highly over-parametrized with respect to the available data, and both parameters and predictions may therefore be arbitrarily uncertain. For this reason, we formally define and analyse the concept of a core prediction. A core prediction is a uniquely identified property that must be fulfilled if the given model structure is to explain the data, even if the individual parameters are non-uniquely identified. It is shown that such a prediction is as strong a conclusion as a rejection. Furthermore, a new method for core prediction analysis is introduced, which is beneficial for the uncertainty of specific model properties, as the method only characterizes the space of acceptable parameters in the relevant directions. This avoids the curse of dimensionality associated with the generic characterizations used by previously proposed methods. Analysis on examples shows that the new method is comparable to profile likelihood with regard to practical identifiability, and thus generalizes profile likelihood to the more general problem of observability. If used, the concepts and methods presented herein make it possible to distinguish between a conclusion and a mere suggestion, which hopefully will contribute to a more justified confidence in systems biology analyses.

Hybrid models and biological model reduction with PyDSTool

The PyDSTool software environment is designed to develop, simulate, and analyze dynamical systems models, particularly for biological applications. Unlike the engineering application focus and graphical specification environments of most general purpose simulation tools, PyDSTool provides a programmatic environment well suited to exploratory data- and hypothesis-driven biological modeling problems. In this work, we show how the environment facilitates the application of hybrid dynamical modeling to the reverse engineering of complex biophysical dynamics; in this case, of an excitable membrane. The example demonstrates how the software provides novel tools that support the inference and validation of mechanistic hypotheses and the inclusion of data constraints in both quantitative and qualitative ways. The biophysical application is broadly relevant to models in the biosciences. The open source and platform-independent PyDSTool package is freely available under the BSD license from http://sourceforge.net/projects/pydstool/. The hosting service provides links to documentation and online forums for user support.

A Bayesian approach to targeted experiment design

Motivation: Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical methods can be used to select experiments that will reduce such uncertainty in an optimal manner. However, existing methods for optimal experiment design (OED) rely on assumptions that are inappropriate when data are scarce considering model complexity.

Results: We have developed a novel method to perform OED for models that cope with large parameter uncertainty. We employ a Bayesian approach involving importance sampling of the posterior predictive distribution to predict the efficacy of a new measurement at reducing the uncertainty of a selected prediction. We demonstrate the method by applying it to a case where we show that specific combinations of experiments result in more precise predictions.

Availability and implementation: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html

Contact:j.vanlier@tue.nl; N.A.W.v.Riel@tue.nl

Supplementary information:Supplementary data are available at Bioinformatics online.

An integrated strategy for prediction uncertainty analysis

Motivation: To further our understanding of the mechanisms underlying biochemical pathways mathematical modelling is used. Since many parameter values are unknown they need to be estimated using experimental observations. The complexity of models necessary to describe biological pathways in combination with the limited amount of quantitative data results in large parameter uncertainty which propagates into model predictions. Therefore prediction uncertainty analysis is an important topic that needs to be addressed in Systems Biology modelling.

Results: We propose a strategy for model prediction uncertainty analysis by integrating profile likelihood analysis with Bayesian estimation. Our method is illustrated with an application to a model of the JAK-STAT signalling pathway. The analysis identified predictions on unobserved variables that could be made with a high level of confidence, despite that some parameters were non-identifiable.

Availability and implementation: Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html.

Contact:j.vanlier@tue.nl

Supplementary information:Supplementary data are available at Bioinformatics online.

Compartmentation of glycogen metabolism revealed from 13C isotopologue distributions

Background

Stable isotope tracers are used to assess metabolic flux profiles in living cells. The existing methods of measurement average out the isotopic isomer distribution in metabolites throughout the cell, whereas the knowledge of compartmental organization of analyzed pathways is crucial for the evaluation of true fluxes. That is why we accepted a challenge to create a software tool that allows deciphering the compartmentation of metabolites based on the analysis of average isotopic isomer distribution.

Results

The software Isodyn, which simulates the dynamics of isotopic isomer distribution in central metabolic pathways, was supplemented by algorithms facilitating the transition between various analyzed metabolic schemes, and by the tools for model discrimination. It simulated ¹³C isotope distributions in glucose, lactate, glutamate and glycogen, measured by mass spectrometry after incubation of hepatocytes in the presence of only labeled glucose or glucose and lactate together (with label either in glucose or lactate). The simulations assumed either a single intracellular hexose phosphate pool, or also channeling of hexose phosphates resulting in a different isotopic composition of glycogen. Model discrimination test was applied to check the consistency of both models with experimental data. Metabolic flux profiles, evaluated with the accepted model that assumes channeling, revealed the range of changes in metabolic fluxes in liver cells.

Conclusions

The analysis of compartmentation of metabolic networks based on the measured ¹³C distribution was included in Isodyn as a routine procedure. The advantage of this implementation is that, being a part of evaluation of metabolic fluxes, it does not require additional experiments to study metabolic compartmentation. The analysis of experimental data revealed that the distribution of measured ¹³C-labeled glucose metabolites is inconsistent with the idea of perfect mixing of hexose phosphates in cytosol. In contrast, the observed distribution indicates the presence of a separate pool of hexose phosphates that is channeled towards glycogen synthesis.

The Virtual Physiological Human

The Virtual Physiological Human is synonymous with a programme in computational biomedicine that aims to develop a framework of methods and technologies to investigate the human body as a whole. It is predicated on the transformational character of information technology, brought to bear on that most crucial of human concerns, our own health and well-being.