@article{nguyen_jameson_baldwin_nardini_smith_haugh_flores_2024, title={Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling}, volume={370}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2024.109158}, abstractNote={Fibroblasts in a confluent monolayer are known to adopt elongated morphologies in which cells are oriented parallel to their neighbors. We collected and analyzed new microscopy movies to show that confluent fibroblasts are motile and that neighboring cells often move in anti-parallel directions in a collective motion phenomenon we refer to as "fluidization" of the cell population. We used machine learning to perform cell tracking for each movie and then leveraged topological data analysis (TDA) to show that time-varying point-clouds generated by the tracks contain significant topological information content that is driven by fluidization, i.e., the anti-parallel movement of individual neighboring cells and neighboring groups of cells over long distances. We then utilized the TDA summaries extracted from each movie to perform Bayesian parameter estimation for the D'Orsgona model, an agent-based model (ABM) known to produce a wide array of different patterns, including patterns that are qualitatively similar to fluidization. Although the D'Orsgona ABM is a phenomenological model that only describes inter-cellular attraction and repulsion, the estimated region of D'Orsogna model parameter space was consistent across all movies, suggesting that a specific level of inter-cellular repulsion force at close range may be a mechanism that helps drive fluidization patterns in confluent mesenchymal cell populations.}, journal={MATHEMATICAL BIOSCIENCES}, author={Nguyen, Kyle C. and Jameson, Carter D. and Baldwin, Scott A. and Nardini, John T. and Smith, Ralph C. and Haugh, Jason M. and Flores, Kevin B.}, year={2024}, month={Apr} }
 @article{nguyen_rutter_flores_2023, title={Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data}, volume={85}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-023-01162-3}, abstractNote={Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models’ performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions.}, number={7}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Nguyen, Kyle and Rutter, Erica M. and Flores, Kevin B.}, year={2023}, month={Jul} }
 @article{nguyen_li_flores_tomaras_dennison_mccarthy_2023, title={Parameter estimation and identifiability analysis for a bivalent analyte model of monoclonal antibody-antigen binding}, volume={679}, ISSN={["1096-0309"]}, DOI={10.1016/j.ab.2023.115263}, abstractNote={Surface plasmon resonance (SPR) is an extensively used technique to characterize antigen-antibody interactions. Affinity measurements by SPR typically involve testing the binding of antigen in solution to monoclonal antibodies (mAbs) immobilized on a chip and fitting the kinetics data using 1:1 Langmuir binding model to derive rate constants. However, when it is necessary to immobilize antigens instead of the mAbs, a bivalent analyte (1:2) binding model is required for kinetics analysis. This model is lacking in data analysis packages associated with high throughput SPR instruments and the packages containing this model do not explore multiple local minima and parameter identifiability issues that are common in non-linear optimization. Therefore, we developed a method to use a system of ordinary differential equations for analyzing 1:2 binding kinetics data. Salient features of this method include a grid search on parameter initialization and a profile likelihood approach to determine parameter identifiability. Using this method we found a non-identifiable parameter in data set collected under the standard experimental design. A simulation-guided improved experimental design led to reliable estimation of all rate constants. The method and approach developed here for analyzing 1:2 binding kinetics data will be valuable for expeditious therapeutic antibody discovery research.}, journal={ANALYTICAL BIOCHEMISTRY}, author={Nguyen, Kyle and Li, Kan and Flores, Kevin and Tomaras, Georgia D. and Dennison, S. Moses and McCarthy, Janice M.}, year={2023}, month={Oct} }