MS03 - MFBM-06

Using Sensitivity Analysis and Uncertainty Quantification to Develop or Improve Biomathematical Models

Tuesday, July 15 at 10:20am

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Kelsey Gasior (University of Notre Dame)

Description:

Developing biomathematical models creates a paradox when determining how best to capture a system’s behavior. Too little information creates uninformative models while too many terms results in overparameterization. Further complications occur with the inclusion of measured, experimental data. Understanding the data presented, as well as the model constructed, means that we need to balance the complexity of the model with the information content in the data. In these situations, we often turn to sensitivity analysis. Sensitivity analysis is an important tool when faced with the inability to uniquely determine parameters from existing datasets, known as parameter identifiability. Additionally, it can help us identify the most influential parameters, test the robustness of our models, and improve our understanding of the system’s behavior. The work presented in this minisymposium will discuss the use of novel methodologies in sensitivity analysis and uncertainty quantification to develop biologically relevant biomathematical models. While the biological applications include epithelial intracellular dynamics, bacterial persistence, ecology, and epidemiology, this session aims to connect researchers interested in parameter estimation, sensitivity analysis, and uncertainty quantification. Discussing the development and relevance of these tools on different biological topics will ultimately spark conversations about the needs and future directions for method development.

Samuel Oliver

Swansea University

"The role of EMT in Ovarian Cancer: Insights from a Mathematical Model"

The role of EMT in Ovarian Cancer: Insights from a Mathematical Model Epithelial-to-mesenchymal transition (EMT) is a critical process in cancer progression that can significantly reduce the effectiveness of treatments. EMT occurs when cells undergo phenotypic changes, resulting in altered behaviours compared to their original state. This transition may lead to increased drug resistance, greater cell plasticity, and enhanced metastatic potential. As a result, understanding and studying the role of EMT in tumour progression and treatment response is essential. In this study, we utilise a 3D agent-based multiscale modelling framework with PhysiCell to examine the role of EMT over time in two ovarian cancer cell lines, OVCAR-3 and SKOV-3. This approach enables us to investigate the spatiotemporal dynamics of ovarian cancer and provide insights into the development of the tumours. The model incorporates microenvironmental conditions, adjusting cellular behaviours based on factors such as substrate concentrations and the proximity of neighbouring cells. The OVCAR-3 and SKOV-3 cell lines exhibit significantly different tumour architectures, allowing for the exploration of various tumour dynamics and morphologies. The model successfully captures biological patterns observed in tumour growth and progression, offering valuable insights into the dynamics of these cell lines. Additionally, sensitivity analysis is conducted to evaluate the impact of parameter variations on model outcomes.

Nate Kornetzke

University of New Mexico

"Turn down that noise! Uncertainty quantification for stochastic models of emerging infectious pathogens"

Emerging infectious pathogens are a persistent public health threat that challenge traditional mechanistic modeling approaches. As outbreaks initially start with a low number of infected hosts, the dynamics of these outbreaks are highly stochastic, making traditional deterministic methods, e.g. ordinary differential equations, unable to qualitatively or quantitatively capture the transmission dynamics. Instead, stochastic models are used, such as Markov chain models, but these models present their own challenges. Often, to infer a quantity of interest with these stochastic models, we need to sample the model’s distribution many times over, introducing an additional source of noise to our analysis. This additional noise can be amplified around bifurcating points of the model, making the inference of our quantity of interest even more difficult. Here, we show how novel tools from the field of uncertainty quantification can be used to disentangle noise in stochastic systems to make rigorous statistical inferences that are crucial for modeling emerging pathogens. We illustrate these techniques with a model of yellow fever virus spillover in the Americas, a virus that has seen rapid emergence amongst multiple hosts and vectors in South America over the last decade.

Steve Williams

University of California, Merced

"Examining models of phenotype selection in populations of bacteria under external predatory stress"

Biofilms are dense communities of bacteria living in a collective extracellular matrix. They aid their constituent bacteria by protecting them from external environmental threats, distributing metabolic workload, and performing complex multicellular processes (e.g., quorum sensing). However, for many organisms, retaining the tools necessary to be multiple phenotypes within their lifetime has been essential for survival. It is natural to wonder how external stressors in marine environments can impact the biofilm formation process and whether these impacts have downstream implications for their participation in multi-organism relationships. To explore this adaptation process, we have employed a previously proposed population model in which bacteria transition freely between planktonic and biofilm phenotypes in the presence of predator. By employing several sensitivity analysis techniques, we probe the parameter space to understand the impacts that changing bacterial dynamics can have. Using synthetic data, we have quantified uncertainties present in the realization of our system using practical identifiability techniques. Finally, we propose a new model with parameter variations within the bacterial population, particularly their ability to attach to biofilms. Through the lens of sensitivity analysis again, this model allows us to begin to measure the rate of adaptation for such populations in terms of the size of the external stressors and the distribution of the variation inside the population.

Kelsey Gasior

University of Notre Dame

"Comparative Sensitivity Analyses and Modeling the Epithelial Mesenchymal Transition"

The epithelial mesenchymal transition (EMT) is a process that allows carcinoma cells to lose their adhesivity and migrate away from a tumor. Further, cells can maintain this invasiveness after they leave their original microenvironment, suggesting that there is an underlying bistable switch. We developed a mathematical model that examined the relationships between E-cadherin and Slug and their responses to tumor-level factors, such as cell-cell contact and TGF-b. Phenomenological model behavior was derived from biological experiments and, ultimately, this model showed how cells at different positions within a tumor can use exogenous factors to undergo EMT. However, the nonlinear dynamics and estimated model parameters make it challenging to analyze and understand what parameters contribute to the observed E-cadherin and Slug changes. Thus, we turn to sensitivity analysis. This work seeks to understand the true impact of mathematical and statistical techniques on our understanding of the dynamics underlying EMT. To provide an extensive understanding, multiple ranges were examined for each parameter and techniques such as nondimensionalization, Latin Hypercube Sampling, Partial Rank Correlation Coefficient, Morris Method Screening, and Sobol’ analysis were used. This wide range of techniques was applied to cells exposed to different levels of cell-cell contact and exogenous TGF-b. By comparing these different methodologies, parameter ranges, and treatment groups, a dual biological and mathematical perspectives emerge. While the different analytical techniques highlight different parameters of importance and interacting relationships, comparing across treatment groups shows how a cell’s identity can be controlled by different intracellular factors, which may shift in the dynamic tumor environment. Together, these results highlight the need for extensive and methodical approach to sensitivity analysis before conclusions can be reached to inform future experiments.

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Annual Meeting for the Society for Mathematical Biology, 2025.