MFBM Subgroup Contributed Talks

Connor McShaffrey

Indiana University Bloomington

"Decomposing Viability Space"

When trying to model how an organism will fare in a particular environment, we need to be able to capture the potential dynamics of the system as well as the survival outcomes they lead to. A growing body of work has been approaching this problem by building dynamical systems models with imposed viability limits, which separate living and terminal states. Since the viability limits are not implicit in the equations that govern the dynamics, there is no guaranteed correspondence between the phase portrait and which initial conditions will remain viable. This means that the topology demands a richer set of analyses, which we refer to as characterizing viability space. Here we will set the groundwork for this methodology, including criteria for novel bifurcations, using a simple mass-action protocell model.
Additional authors: Randall Beer (Indiana University Bloomington)

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Holly Huber

University of Southern California

"Systematic Bayesian Posterior Analysis Facilitates Hypothesis Formation and Guides Investigation of Pancreatic Beta Cell Signaling"

Intracellular protein dynamics can be simulated with a system of ordinary differential equations, where parameters represent reaction rate constants and initial protein concentrations. Such mechanistic models formalize the biological hypotheses they’re based on. Bayesian inference fits the posterior distribution of model parameters to data; evidence of alternative hypotheses can manifest in the posterior and serve as a starting point for hypothesis refinement. However, existing approaches to search for such evidence are largely ungeneralizable and unsystematic, limiting their scalability. Here, we show that ranking marginal posteriors by information gained from experimental data provides a systematic and generalizable way to search for alternative hypothesis evidence. Rather than searching for evidence at random, one can search per the ranking. We subsequently use this approach to refine our understanding of pancreatic beta cell signaling dynamics, which regulate beta cell proliferation.

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Nathaniel Linden

University of California San Diego

"Multimodel modeling for blood glucose and insulin measurements in diabetes"

Uncertainty in a model formulation due to differing assumptions or unknown system mechanisms is often overlooked when applying mathematical models in biology and medicine. In diabetes diagnostics, mathematical models have long been used to make inferences about a patient’s metabolic health using available clinical data such as blood glucose measurements over time. These approaches often rely on a phenomenological model to approximate the physiological system, ignoring possible uncertainty in the model structure. However, there are usually several possible phenomenological models, each of which uses different formulations to represent the same biological processes. Given a family of phenomenological models, one typically chooses a single model based on a priori assumptions. In this work, we instead focus on leveraging the whole family of models to develop robust predictors in the face of uncertainty in the models describing the biological process. We explore several approaches to average the predictions from all available models, including Bayesian model averaging and probability distribution fusion. These methods allow us to construct robust predictors using the entire model family and reduce biases associated with choosing a single best model. As a test case, we chose the prediction of beta cell insulin regulation and associated diagnostic metrics from blood glucose measurements. Our results show that working with a family of models instead of a single model improves the certainty of modeling-based predictions, reduces biases associated with selecting one model, and explicitly accounts for model uncertainty.
Additional authors: Boris Kramer - University of California San Diego Mechanical and Aerospace Engineering; Padmini Rangamani - University of California San Diego Mechanical and Aerospace Engineering

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Robert DeJaco

National Institute of Standards and Technology

"Reducing Bias and Quantifying Uncertainty in Fluorescence Produced By PCR"

We present a new approach for relating nucleic-acid content to fluorescence in a real-time Polymerase Chain Reaction (PCR) assay. By coupling a two-type stochastic branching process for PCR with a fluorescence analog of Beer’s Law, the approach reduces bias and quantifies uncertainty in fluorescence. As the two-type branching process distinguishes between complementary strands of DNA, it allows for a stoichiometric description of reactions between fluorescent probes and DNA and can capture the initial conditions encountered in assays targeting RNA. Analysis of the expected copy-number identifies additional dynamics occurring at short times (or, equivalently, low cycle numbers), while investigation of the variance reveals the contributions from liquid volume transfer, imperfect amplification, and strand-specific amplification (i.e., if one strand is synthesized more efficiently than its complement). Linking the branching process to fluorescence by the Beer’s Law analog allows for a more objective and a priori description of background fluorescence. It also enables uncertainty quantification (UQ) in fluorescence which, in turn, leads to analytical relationships between amplification efficiency (probability) and limit of detection. This work sets the stage for UQ-PCR, where both the input copy-number and its uncertainty are quantified from fluorescence measurements.
Additional authors: Matthew J. Roberts, Applied and Computational Mathematics Division, National Institute of Standards and Technology; Erica L. Romsos, Biomolecular Measurement Division, National Institute of Standards and Technology; Peter M. Vallone, Biomolecular Measurement Division, National Institute of Standards and Technology; Anthony J. Kearsley, Applied and Computational Mathematics Division, National Institute of Standards and Technology;

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