Microtubules are protein polymers comprised of tubulin, which are polarized and facilitate intracellular transport. A stable microtubule structure is important to ensure the long-term survival of neurons. However, microtubules also need to be dynamic and reorganize in response to injury events, which results in an increase in microtubule dynamics. How this complex balance is achieved on...
Mechanical properties of molecular motors such as kinesin are often measured using optical traps. We develop three-dimensional stochastic models based on force and torque balances for two experimental setups: the single-bead assay and the three-bead assay. Our goal is to provide insight into how modeling choices in forceโvelocity and forceโdetachment relationships influence motion along the...
Understanding how epidemics spread on contact networks when the data are incomplete remains one of the central challenges in mathematical epidemiology. In this talk, I will describe a framework for analyzing stochastic epidemic models under partial observation, combining ideas from dynamical survival analysis (DSA), pairwise survival models, and recent exact closure results for SIR dynamics on...
I will discuss the use of diffusion models for particle tracking microscopy images. The goal is to have a fully integrated generative model that connects stochastic models of particle motion to microscopy image data. Unfortunately, the observation likelihood function is too complex to explicitly model, and we do not know this function. Learning the likelihood function from a suitably large...
A common challenge in mathematical biology arises from data collected from a biological system for which we have a mechanistic model, such as an ODE model. Identifying the parameters of the model is often done through estimation schemes such as non-linear least squares, which presume errors in the amplitude of the data. Such estimation can be challenging, and other sources of error, such as...
Changepoint detection seeks to identify structural breaks in sequential data, often arising as noisy observations of underlying stochastic dynamical systems. However, exact likelihood-based methods can be computationally expensive, particularly in large-scale settings. We study maximum likelihood estimation for multiple changepoint models under possible overfitting and show that, even when the...
In the last couple of years, I have noticed an emerging theme in my work. Across multiple biological systems, colleagues and I have articulated models that involve particles that (1) emerge at random times from a fixed source-location distribution; (2) move throughout a local environment randomly (either diffusing, or switching between deterministic states); and (3) are removed from the system...
Data collection for biological systems has undergone a revolution over the past few decades with electronic trackers for wildlife populations giving us minute to minute information about their locations and fluorescence data at the cellular level tracking the number and location of proteins. On the theory side, we have well-known population models for the interaction of wildlife and also for...
