Date of Graduation
2015
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Adam M Halasz
Committee Co-Chair
Harvey Diamond
Committee Member
Jeremy S Edwards
Committee Member
Hong Jian Lai
Committee Member
Adrian Tudorascu
Abstract
Membrane receptors are specialized membrane-bound proteins that facilitate communication be- tween the intracellular and extracellular membrane. They control signal initiation in many im- portant cellular signaling pathways. Cell signaling (or signal transduction) provides the logical inputs individual cells need in order to perform their role in the context of the organism. Signal- ing molecules such as hormones, neurotransmitters or growth factors, are secreted by cells in the organism as a result of certain conditions; the cells receiving the signal change (or maintain) their state in response to the signaling input. The incoming information is processed and the response is formulated by a complex bio-molecular network.;For many ligand / receptor families, receptor dimerization or cross-linking is a necessary step for activation, making signaling pathways sensitive to the distribution of receptors in the membrane. Microscopic imaging and modern labeling techniques reveal that certain receptor types tend to co-localize in clusters. The origin of these clusters is not well understood; they are likely not the result of chemical binding, but of a pre-existing micro-domain structure of the membrane. In this work, we analyze a set of micrographs resulting from a study of vascular endothelial growth factor (VEGF) receptor. VEGF is a protein that is involved in the process of the growth and maintenance of blood vessels. The micrographs represent static snapshots of VEGF receptors. They are obtained by fixing the cells from a cell culture, separating their cell membrane, and then labeling the receptors with nano-gold particles. The samples are then imaged by high-resolution transmission electron microscopy (TEM).;The first part of the work presented here consists of characterizing the two dimensional point di- stirbutions obtained by identifying the location of the labelled receptor particles. We first applied a number of statistical tests used to establish whether the distributions are consistent with random placement, and whether clustering was present. After establishing the presence of clustering in vir- tually all images, we proceeded to separate the points in each image into clusters using hierarchic distance based clustering. This method relies on a characteristic length scale that is not a priori identified. Building on previous work, we developed a more refined approach to the identification of an optimal length parameter. We implemented this approach to cluster identification as well as a procedure that assigns a geometric shape to each cluster, in computer script that performs all of these analyses for a set of files. Using the analysis pipeline, we processed approximately 80 images that were available and summarized a number of image parameters, measures of clustering, as well as distributions of cluster sizes.;The second part of the dissertation aims to develop and validate a stochastic model of clustering, based on the hypothesis of pre-existing domains that have a high affinity for receptors. The proxi- mate objective is to clarify the mechanism behind cluster formation, and in the longer perspective, to estimate the effect on signaling. We showed that the observed particle distribution results were consistent with the random placement of receptors within the clusters and, to a lesser extent, the random placement of the clusters on the cell membrane. We then defined a simple statistical model, based on the pre-existing domain hypothesis, to predict the probability distribution of cluster sizes.;The model parameters can be identified by fitting to the experimentally derived cluster size distri- butions. Using a Metropolis-Hastings algorithm, we found that the majority of the images (close to 75%) could be fit individually. The remaining images exhibited large scale features that were not meant to be captured in the model. The global fit of the 60 images with a single model pa- rameter set was less successful. We obtained better results by separating the images into groups using k-means clustering, and then performing global fits to each group taken separately. The bi- ological significance of these emerging groups is not clear at the moment; however, the process yielded sets of parameter values that can readily be used in dynamical calculations as estimates of the quantitative characteristics of the clustering domains.
Recommended Citation
Guven, Emine, "Validation of an Experimentally Motivated Predictive Model for the Spontaneous Clustering of Receptors on the Cell Membrane" (2015). Graduate Theses, Dissertations, and Problem Reports. 5726.
https://researchrepository.wvu.edu/etd/5726