Uncertainty plays a major role in using mathematics to address biological and medical questions, specifically when analyzing real-world data. This minisymposium features recent mathematical and computational advances in solving inverse problems and quantifying uncertainties for a wide variety of biological and biomedical applications. Topics include development of numerical methods, model reduction, parameter estimation, and data-driven approaches for applications such as safety pharmacology, cell metabolism, tumor growth, and blood coagulation.
14:00
Bayesian uncertainty quantification for particle-based simulation of lipid bilayer membranes
Anastasios Matzavinos | Brown University | United States
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Anastasios Matzavinos | Brown University | United States
A number of problems of interest in applied mathematics and biology involve the quantification of uncertainty in computational and real-world models. A recent approach to Bayesian uncertainty quantification using transitional Markov chain Monte Carlo (TMCMC) is extremely parallelizable and has opened the door to a variety of applications which were previously too computationally intensive to be practical. In this talk, we first explore the machinery required to understand and implement Bayesian uncertainty quantification using TMCMC. We then describe dissipative particle dynamics, a computational particle simulation method which is suitable for modeling biological structures on the subcellular level, and develop an example simulation of a lipid membrane in fluid. Finally, we apply the algorithm to a basic model of uncertainty in our lipid simulation, effectively recovering a target set of parameters (along with distributions corresponding to the uncertainty) and demonstrating the practicality of Bayesian uncertainty quantification for complex particle simulations.
14:30
- CANCELED - Model uncertainties in gas transport to cells
Erkki Somersalo | Case Western Reserve University | United States
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Erkki Somersalo | Case Western Reserve University | United States
According to the prevalent paradigm, gas transport through cell membranes takes place through diffusion process. Recent experiments confirm that certain membrane-bound proteins, the aquaporins (AQP) foremost, play a significant role by providing a preferred channel for gases, thus calling for novel models for the transport. In this talk, some of the recent modeling work is reviewed, including a discussion of estimating the model parameters under the model uncertainties.
15:00
Experimental design and identifiability in models of blood coagulation
Laura Albrecht | Colorado School of Mines | United States
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Karin Leiderman | Colorado School of Mines | United States
Laura Albrecht | Colorado School of Mines | United States
Dougald Monroe | University of North Carolina, Chapel Hill | United States
Suzanne Sindi | University of California, Merced | United States
Douglas Nychka | Colorado School of Mines | United States
Blood coagulation is a complex network of biochemical reactions necessary for blood clots to form. To combat or enhance clotting, components of the coagulation system can be targeted by therapeutic agents, the kinetic properties of which are studied using indirect measurements of enzymatic activity and inhibition via synthetic substrates in biochemical assays. Mathematical models are thus indispensable tools that allow for interpretation of such data, elucidation of biochemical mechanisms, and experimental design. In particular, systems of nonlinear ODEs give interpretable rate equations and allow for data fitting. We recently used Bayesian parameter estimation to determine that product inhibition plays an important role in even the simplest of biochemical assays that use synthetic substrates. In this work, as a first step toward modeling more complex reactions, we consider multiple enzymes and inhibitors in the assays, for which the kinetic parameters, initial concentrations, and kinetic schemes are uncertain. It is well known that parameters in these systems can be difficult to estimate or possibly not even identifiable. The challenge is to formulate an accurate biochemical model and identify the specific experimental designs that will result in useful estimates of the process parameters. Some promising results have been obtained using Monte Carlo simulations of synthetic observations and then examining profile likelihoods to determine the identifiability of parameters.
15:30
Contrasting Sensitivity and Data Assimilation in the Context of the Autoimmune Disease Alopecia Areata
Nick Cogan | Florida State University | United States
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Nick Cogan | Florida State University | United States
Atanaska Dobreva | North Carolina State University | United States
Feng Bao | Florida State University | United States
Ralf Paus | University of Miami Miller School of Medicine | United States
Alopecia Areata (AA) is an autoimmune disease characterized by hair loss, often in distinct spatial patches. Hair follicles are one of the few immune privilege sites — meaning foreign antigens do not elicit an immune response. The cause of AA is thought to be a catastrophic loss of immune suppression through an autoimmune guardian mechanism. We have previously developed a model that characterizes the dynamics of a both single hair follicles and larger patches of follicles, the immune guardian mechanism, and the immune system response. The model captures key characteristics of the disease and sensitivity analysis shows that there are specific processes that play a district role in the progression of the hair loss patches. Recently we began studying the inverse problem associated with taking partial observations that might be made in a clinic to estimate the disease state. Using synthetic data, we show that the data assimilation method capitalizes on sensitivity to enhance the convergence to true parameters. This is a non-intuitive result since sensitive parameters are often difficult to estimate with other methods.