Doctor of Philosophy

dissertationThe efficient transport of particles throughout a cell plays a fundamental role in several cellular processes. Broadly speaking, intracellular transport can be divided into two categories: passive and active transport. Whereas passive transport generally occurs via diffusive processes, active transport requires cellular energy through adenosine triphosphate (ATP). Many active transport processes are driven by molecular motors such as kinesin and dynein, which carry cargo and travel along the microtubules of a cell to deliver specific material to specific locations. Breakdown of molecular motor delivery is correlated with the onset of several diseases, such as Alzheimer's and Parkinson's. We mathematically model two fundamental cellular processes. In the first part, we introduce a possible biophysical mechanism by which cells attain uniformity in vesicle density throughout their body. We do this by modeling bulk motor density dynamics using partial differential equations derived from microscopic descriptions of individual motor-cargo complex dynamics. We then consider the cases where delivery of cargo to cellular targets is (i) irreversible and (ii) reversible. This problem is studied on the semi-infinite interval, disk, and spherical domains. We also consider the case where exclusion effects come into play. In all cases, we find that allowing for reversibility in cargo delivery to cellular targets allows for more uniform vesicle distribution. In the second part, we see how active transport by molecular motors allows for length control and sensing in flagella and axons, respectively. For the flagellum, we model length control using a doubly stochastic Poisson model. For axons, we model bulk motor dynamics by partial differential equations, and show how spatial information may be encoded in the frequency of an oscillating chemical signal being carried by dynein motors. Furthermore, we discuss how frequency-encoded signals may be decoded by cells, and how these mechanisms break down in the face of noise

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.Comment: updated: 13 pages, 5 figure

Correlated Information Reduces Accuracy of Pioneering Decision-Makers

Normative models are often used to describe how humans and animals make decisions. These models treat deliberation as the accumulation of uncertain evidence that terminates with a commitment to a choice. When extended to social groups, such models often assume that individuals make independent observations. However, individuals typically gather evidence from common sources, and their observations are rarely independent. Here we ask: For a group of ideal observers who do not exchange information, what is the impact of correlated evidence on decision accuracy? We show that even when agents are identical, correlated evidence causes decision accuracy to depend on temporal decision order. Surprisingly, the first decider is less accurate than a lone observer. Early deciders are less accurate than late deciders. These phenomena occur despite the fact that the rational observers use the same decision criterion, so they are equally confident in their decisions. We analyze discrete and continuum evidence-gathering models to explain why the first decider is less accurate than a lone observer when evidence is correlated. Pooling the decisions of early deciders using a majority rule does not rescue accuracy in the sense that such pooling results in only modest accuracy gain. Although we analyze an idealized model, we believe that our analysis offers insights that do not depend on exactly how groups integrate evidence and form decisions.Comment: 19 pages, 5 figure

Boundary-driven emergent spatiotemporal order in growing microbial colonies

Non UBCUnreviewedAuthor affiliation: University of HoustonPostdoctora

A frequency-dependent decoding mechanism for axonal length sensing

We have recently developed a mathematical model of axonal length sensingin which a system of delay differential equations describe a chemical signaling network. We showed that chemical oscillations emerge due to delayed negative feedback via a Hopf bifurcation, resulting in a frequency that is a monotonically decreasing function of axonal length. In this paper, we explore how frequency-encoding of axonal length can be decoded by a frequency-modulated gene network. If the protein output were thresholded, then this could provide a mechanism for axonal length control. We analyze the robustness of such a mechanism in the presence of intrinsic noise due to finite copy numbers within the gene network

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems.

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics