Doubly stochastic Poisson model of flagellar length control

We construct and analyze a stochastic model of eukaryotic flagellar length control. Flagella are microtubule-based structures that extend to about 10 μ m from the cell and are surrounded by an extension of the plasma membrane. Flagellar length control is a particularly convenient system for studying organelle size regulation since a flagellum can be treated as a one-dimensional structure whose size is characterized by a single length variable. The length of a eukaryotic flagellum is important for proper cell motility, and a number of human diseases appear to be correlated with abnormal flagellar lengths. Flagellar length control is mediated by intraflagellar transport (IFT) particles, which are large motor protein complexes within a flagellum that transport tubulin (the basic building block of microtubules) to the tip of the flagellum. The critical length of the flagellum is thus thought to be determined by the dynamical balance between length-dependent transport and assembly of microtubules and length-independent disassembly at the tip. In our model we assume that IFT particles are injected into a flagellum according to a Poisson process, with a rate that depends on a second stochastic process associated with the binding and unbinding of IFTs to sites at the base of the flagellum. The model is thus an example of a doubly stochastic Poisson process (DSPP), also known as a Cox process. We use the theory of DSPPs to analyze the effects of fluctuations on IFT and show how our model captures some of the features of experimental time series data on the import of IFT particles into flagella. We also indicate how DSPPs provide a framework for developing more complex models of IFT

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

Doctor of Philosophy

dissertationWe analyze different models of several chemical reactions. We find that, for some reactions, the steady state behavior of the chemical master equation, which describes the continuous time, discrete state Markov process, is poorly approximated by the deterministic model derived from the law of mass action or a mean field model derived in a similar way. We show that certain simple enzymatic reactions have bimodal stationary distributions in appropriate parameter ranges, though the deterministic and mean field models for these reactions do not have the capacity to admit multiple equilibrium points no matter the choice of rate constants. We provide power series expansions for these bimodal distributions. We also consider several variants of an autocatalytic reaction. This reaction's deterministic model predicts a unique positive stable equilibrium, but the only stationary distribution of its chemical master equation predicts extinction of the autocatalytic chemical species with probability 1. We show that the transient distribution of this chemical master equation is centered near the deterministic equilibrium and that the stationary distribution is only reached on a much longer time scale. Finally, we consider a model for the rotational direction switching of the bacterial rotary motor and propose two possible reductions for the state space of the corresponding Markov chain. One reduction, a mean field approximation, is unable to produce physically realistic phenomena. The other reduction retains the properties of interest in the system while significantly decreasing the computation required for analysis. We use this second reduction to fit parameters for the full stochastic system and suggest a mechanism for the sensitivity of the switch

Biophysical methods bridging signal pathway architecture and dynamics in multigenerational bacterial processes

Cells sense their environment and process changes through intracellular signaling networks to coordinate behavioral changes, such as cell fate decisions. In bacterial systems, these changes often occur over time periods longer than a single cell cycle. While we are now able to experimentally track and monitor these behavioral changes over multiple generations, we have a limited conceptual understanding of how these decisions are mediated by signaling pathways. Here, I present two projects that build predictive frameworks for understanding signaling pathway dynamics over multiple generations informed by the signal network architectures. In the first section, I use computational simulations to understand how signaling pathway architecture controls the duration over which related cells maintain similar concentrations of signaling pathway components following division from a common mother cell. I find that signal amplification is a requirement for similarity between related cells. In the second section, I take a joint theory-experiment approach to analyze the accumulation timescale of the signaling molecule cyclic di-GMP during biofilm initiation in the soil bacterium B. subtilis. Here I predict that the accumulation occurs over many generations, suggesting the possibility cyclic di-GMP is used as a cellular timer mechanism during biofilm initiation. These results both explain previous experimental findings as well as generate new predictions for how signaling pathways mediate single-cell behaviors in bacterial populations. Together, my work demonstrates the power of a joint theory-experiment approach to understand the long-term, dynamical behavior of intracellular signaling pathways by linking their architecture to their dynamical function

Signal processing in biological cells : proteins, networks, and models

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 202-210).This thesis introduces systematic engineering principles to model, at different levels of abstraction the information processing in biological cells in order to understand the algorithms implemented by the signaling pathways that perform the processing. An example of how to emulate one of these algorithms in other signal processing contexts is also presented. At a high modeling level, the focus is on the network topology rather than the dynamical properties of the components of the signaling network. In this regime, we examine and analyze the distribution and properties of the network graph. Specifically, we present a global network investigation of the genotype/phenotype data-set recently developed for the yeast Saccharomyces cerevisiae from exposure to DNA damaging agents, enabling explicit study of how protein-protein interaction network characteristics may be associated with phenotypic functional effects. The properties of several functional yeast networks are also compared and a simple method to combine gene expression data with network information is proposed to better predict pathophysiological behavior. At a low level of modeling, the thesis introduces a new framework for modeling cellular signal processing based on interacting Markov chains. This framework provides a unified way to simultaneously capture the stochasticity of signaling networks in individual cells while computing a deterministic solution which provides average behavior. The use of this framework is demonstrated on two classical signaling networks: the mitogen activated protein kinase cascade and the bacterial chemotaxis pathway. The prospects of using cell biology as a metaphor for signal processing are also considered in a preliminary way by presenting a surface mapping algorithm based on bacterial chemotaxis.by Maya Rida Said.Sc.D

Material Theories

The subject of this meeting was mathematical modeling of strongly interacting multi-particle systems that can be interpreted as advanced materials. The main emphasis was placed on contributions attempting to bridge the gap between discrete and continuum approaches, focusing on the multi-scale nature of physical phenomena and bringing new and nontrivial mathematics. The mathematical debates concentrated on nonlinear PDE, stochastic dynamical systems, optimal transportation, calculus of variations and large deviations theory

A Computational Study of E. coli Chemotaxis

Wolde, P.R. ten [Promotor