2022 Theses Doctoral

# Bayesian analysis of particle tracking data using hierarchical models for characterization and design

This dissertation explores the intersection between the fields of colloid science and statistical inference where the stochastic trajectories of colloidal particles are captured by video microscopy, reconstructed using particle tracking algorithms, and analyzed using physics-based models and probabilistic programming techniques. Although these two fields may initially seem disparate, the dynamics of micro- and nano-sized particles dispersed in liquids at room temperature are inherently stochastic due to Brownian motion.

Further, both the particles under observation and their environment are heterogeneous, leading to variability between particles as well. We use Bayesian data analysis to infer the uncertain parameters of physics-based models that describe the observed trajectories, explicitly modeling the hierarchical structure of the noise under a set of varying experimental conditions.

We set the stage in Chapter 1 by introducing Robert Brown's curious observation of incessantly diffusing pollen grains and Albert Einstein's statistical physics model that describes their motion. We analyze Jean Baptiste Perrin's data from Les Atomes using a probabilistic model to infer the uncertain diffusivities of the colloids. We show how the Bayesian paradigm allows us to assign and update our credences, before and after observing this data and quantify the information gained by the observation.

In Chapter 2, we build on these concepts to provide insight on the phenomenon of enhanced enzyme diffusion, whereby enzymes are purported to diffuse faster in the presence of their substrate. We develop a hierarchical model of enzyme diffusion that describes the stochastic dynamics of individual enzymes drawn from a dispersed population. Using this model, we analyze single molecule imaging data of urease enzymes to infer their uncertain diffusivities for different substrate concentrations. Our analysis emphasizes the important role of model criticism for establishing self-consistency between experimental observations and model predictions; moreover, we caution against drawing strong conclusions when such consistency cannot be established.

In Chapter 3, we automate, and optimize the data acquisition process, tuning a resonant acoustic cell using minimal experimental resources. By iterating a cycle of observation, inference, and design, we select the frequency the applied signal and the framerate of the data acquisition, garnering the same amount of information as a grid search approach with a fraction of the data.

Finally, in Chapter 4, we discuss the role of Bayesian inference and design to optimize functional goals and discuss selected examples on where black-box techniques may prove useful. We review the current state of the art for magnetically actuated colloids and pose the search for autonomous magnetic behaviors as a design problem, offering insight as we seek to augment and accelerate the capabilities of micron scale magnetically actuated colloids using modern computational techniques.

## Files

- DhattGauthier_columbia_0054D_17504.pdf application/pdf 9.81 MB Download File

## More About This Work

- Academic Units
- Chemical Engineering
- Thesis Advisors
- Bishop, Kyle J.
- Degree
- Ph.D., Columbia University
- Published Here
- October 12, 2022