Computational Methods for Understanding Dynamics in Mass Transport and Tissue Development

Abstract

Elucidating the process by which a biological system evolves and properly identifying hidden states and influential underlying factors are important for studying biological functions and origins of diseases. However, due to the small length and time scale of many biological systems, these evolution processes are invisible under current microscopy techniques. The goal of this dissertation is to provide mathematical and computational models to help re-construct the dynamics inside biological systems from limited experimental observations and aid the understanding of system properties. Three different types of models were developed using first principles, mathematical abstraction and data-based statistical inference.

To describe the dynamical transport of intracellular cargoes and reveal underlying factors that impair transport efficiency, a multi-physics stochastic model is developed based on first principles and solved by Monte Carlo simulation. In the model, the transport of a cargo by multiple kinesin motors along tracks (microtubules) is simplified as a spherical cargo being moved forward by several non-linear springs along cylindrical and intersecting tracks. The thermal diffusion of cargo, walking motion of motors, and interactions between cargo, motors and tracks are considered based on fundamental physics laws. Using the model, comprehensive collective behaviors of motor kinesins influenced by the topology of tracks were uncovered and studied based on macroscopic experimental observations such as the transport directions and pausing time at track intersections.

To connect the macroscopic particle distribution with its microscopic properties, such as particle moving direction and speed, a generalized random walk model is introduced. Particularly, the influence of directional heterogeneity (i.e. probability of moving along $theta$ direction is non-uniformly distributed between 0 and $2pi$) on particle diffusion coefficient and mean square displacement is studied. We observed that when directional heterogeneity only depends on space, particle performs normal diffusion with directed drifting. Including the correlation between directional persistence (i.e. probability of maintaining current moving direction) and particle speed leads to Fickian but non-Gaussian particle diffusion. Furthermore, the self-reinforced directional persistence leads to superdiffusive motion of particles. The generalized random walk model can be used as a mathematical abstraction of the movements of many biological particles, such as cell migration and intracellular protein diffusion. Given the macroscopic distribution of biological particles, the proposed model provides insights about their moving speed and directional persistence.

In the end, an image-based tissue profiling and trajectory inference algorithm is developed. This algorithm extracts morphological and intensity features from tissue images fixed at discrete time points. By projecting high-dimensional feature data set to new coordinates based on tissue similarities, the algorithm helps reduce systematic noise coming from the tissue heterogeneity and inference a continuous developmental trajectory. Following the trajectory, the bifurcating expressions of proteins were predicted and applied to understand tissue development dynamics. In particular, the developmental progression of embryonic-like tissues, including the morphological changes and appearance of new cell types, are studied based on the algorithm.