Nonlinear Mixed Effects Modeling for Quantifying Variability and Uncertainty in Systems Medicine

Nonlinear mixed effects (NLME) modeling is a well established discipline within quantitative clinical pharmacology, i.e., the integrated study of drug disposition, drug action, and associated variability in humans by means of mathematical models. Recent advances in experimental techniques that allow data collection from individual cells makes it now also possible to also apply NLME modeling to quantify cell-to-cell variability in molecular cell biology. Combining systems biology pathway models based on cellular assay data with quantitative clinical pharmacology models based on clinical data within one and the same computational framework, accounting for both inter-individual and intra-individual variability, has the potential to provide a very valuable tool for systems medicine.

In this talk we will give a brief introduction to NLME modeling of dynamical systems described by ordinary and stochastic differential equations utilizing discrete time observations from a population of subjects. We will also demonstrate the NLMEModeling package for Mathematica, which streamlines the model building process and analysis. Furthermore, the utility of the NLME modeling approach will be shown by means of examples from cell biology and quantitative pharmacology.

Regulating the dynamics of interferon alpha induced antiviral responses

The induction of interferon-mediated responses is the first line of defense against pathogens such as viruses. Yet, the dynamics and extent of interferon alpha (IFNα)-induced antiviral genes vary remarkably and mechanisms that shape these responses are remain incompletely understood.

To unravel mechanisms that determine the sensitivity of hepatocytes to interferon alpha (IFNα), we established an ordinary differential equation model for IFNα signal transduction that comprises multiple feedback regulators. The model-based analysis showed that prestimulation with a low IFNα dose hypersensitizes the pathway, whereas prestimulation with a high dose of IFNα leads to a dose-dependent desensitization. The analysis of patient derived hepaptocytes revealed that the amounts of STAT1, STAT2, IRF9, and USP18 varied substantially between the patients. Interestingly, our studies showed that whereas the basal amount of the negative feedback regulator USP18 determines patient-specific pathway desensitization, it is the abundance of STAT2 that determines the patient specific responses.

To overcome insufficient activation of IFNalpha induced antiviral responses, we next asked whether we could utilize our approach to identify mechanisms to amplify pathway activation. By mathematical modeling we identified mRNA stability as well as a negative regulatory loop as key mechanisms endogenously controlling the expression dynamics of IFNα-induced antiviral genes in hepatocytes. We uncovered that by independent mechanisms the negative feedback regulator IRF2 and the proinflammatory cytokine IL1beta control the strength of elicited responses. Our results show that knock down of IRF2 or even to a larger extent addition of IL1beta result in enhancement of responses including an elevated inhibition of viral replication. Thus, the quantitative knowledge on mechanisms controlling the strength of IFNalpha signal transduction facilitates the prediction of strategies to improve antiviral therapies.

Mark Tomás Mc Auley and Callum Davies

Atherosclerotic cardiovascular disease (ACVD) is the leading cause of morbidity and mortality amongst Western populations. Dysregulated cholesterol metabolism is the principal risk factor for ACVD. Cholesterol metabolism is maintained by an array of complex interacting biological mechanisms. These regulatory processes are multicomponent in nature and display emergent properties. Likewise, the mechanisms which underpin atherogenesis are nontrivial and interact across time and space. Mathematical modelling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering the dynamics of both cholesterol metabolism and atherosclerosis. However, to date no model has successfully integrated cholesterol biosynthesis, whole body metabolism and atherosclerosis. In this work we describe how we merged a model of cholesterol metabolism with a model of atherosclerosis. The SBML encased models were merged in COPASI, which was then utilised to reparametrize and simulate the combined model. Using our novel in silico system we were able to reproduce output from the parent models. As a result, we have created a more complete theoretical representation of cholesterol metabolism and its intersection with atherosclerosis. It is hoped this new system will help us to develop a deeper understanding of the relationship between cholesterol metabolism and ACVD.

Gemma Massonis, Julio Banga and Alejandro Villaverde

Mechanistic dynamic models allow for a quantitative and systematic interpretation of data and the generation of testable hypotheses. However, these models are often over-parameterized, leading to non-identifiability and non-observability, i.e. the impossibility of inferring their parameters and state variables. In many cases, the source of over-parameterization is structural, that is, it stems from the model equations. The lack of structural identifiability and observability (SIO) compromises a model’s ability to make predictions and provide insight. Here we present a methodology, AutoRepar, that corrects SIO deficiencies automatically, yielding reparameterized models that are structurally identifiable and observable [1]. The reparameterization preserves the mechanistic meaning of selected variables, and has the exact same dynamics and input-output mapping as the original model. We implement AutoRepar as an extension of the STRIKE-GOLDD software toolbox for SIO analysis [2], applying it to several models from the literature to demonstrate its ability to repair their structural deficiencies. AutoRepar increases the applicability of mechanistic models, enabling them to provide reliable information about their parameters and dynamics.

[1] Massonis, G., Banga, J. R., & Villaverde, A. F. (2020). Repairing dynamic models: a method to obtain identifiable and observable reparameterizations with mechanistic insights. arXiv preprint arXiv:2012.09826.
[2] Villaverde, A. F., Tsiantis, N., & Banga, J. R. (2019) Full observability and estimation of unknown inputs, states, and parameters of nonlinear biological models. Journal of the Royal Society Interface, 16:20190043 doi:10.1098/rsif.2019.0043

Charles Barker, Eirini Petsalaki, Girolamo Giudice, Emmanuel Ekpenyong, Chris Bakal and Evangelia Petsalaki

Gaining meaningful insights on signaling activity from expression data is fraught with difficulties due to the indirect and non-linear nature through which observed gene expression and signal transduction interact. This is further complicated when we wish to study the signaling processes that regulate complex phenotypes, defined by many features whose complexity renders them ill-suited to be studied by differential expression based methods. Here, we present a protocol for producing phenotype-specific prior knowledge networks, by incorporating context-specific gene expression modules and the transcription factors and pathways that regulate them in a regulatory subnetwork. We illustrate this method by studying the regulatory networks associated with cell shape in breast cancer and show that when perturbed, the kinases within this network have a significant effect on the phenotypes in question. This method is interoperable with any paired phenotype-gene expression data and has utility in defining prior-knowledge networks for the construction of mechanistic models of diverse cellular processes.