Cells can be viewed as sophisticated machines that organize their constituent components and molecules to receive, process, and respond to signals. The goal of the scientist is to uncover both the individual operations underlying these processes and the mechanism of the emergent properties of interest that give rise to the various phenomena such as disease, development, recovery or aging. Cell signaling plays a crucial role in all of these areas. The complexity of biological processes coupled with the physical limitations of experiments to observe individual molecular components across small to large scales limits the knowlege that can be gleaned from direct observations. Mathematical modeling can be used to estimate parameters that are hidden or too difficult to observe in experiments, and it can make qualitative predictions that can distinguish between hypotheses of interest. Statistical analysis can be employed to explore the large amounts of data generated by modern experimental techniques such as sequencing and high-throughput screening, and it can integrate the observations from many individual experiments or even separate studies to generate new hypotheses.
This dissertation employs mathematical and statistical analyses for three prominent aspects of cell signaling: the physical transfer of signaling molecules between cells, the intracellular protein machinery that organizes into pathways to process these signals, and changes in gene expression in response to cell signaling. Computational biology can be described as an applied discipline in that it aims to further the knowledge of a discipline that is distinct from itself. However, the richness of the problems encountered in biology requires continuous development of better methods equipped to handle the complexity, size, or uncertainty of the data, and to build in constraints motivated by the reality of the underlying biological system. In addition, better computational and mathematical methods are also needed to model the emergent behavior that arises from many components. The work presented in this dissertation fulfills both of these roles. We apply known and existing techniques to analyse experimental data and provide biological meaning, and we also develop new statistical and mathematical models that add to the knowledge and practice of computational biology.
Much of cell signaling is initiated by signal transduction from the exterior, either by sensing the environmental conditions or the recpetion of specific signals from other cells. The phenomena of most immediate concern to our species, that of human health and disease, are usually also generated from, and manifest in, our tissues and organs due to the interaction and signaling between cells. A modality of inter-cellular communication that was regarded earlier as an obscure phenomenon but has more recently come to the attention of the scientific community is that of tunneling nanotubes (TNs). TNs have been observed as thin (of the order of 100 nanometers) extensions from a cell to another closely located one. The formation of such structures along with the intercellular exchange of molecules through them, and their interaction with the cytoskeleton, could be involved in many important processes, such as tissue formation and cancer growth. We describe a simple model of passive transport of molecules between cells due to TNs. Building on a few basic assumptions, we derive parametrized, closed-form expressions to describe the concentration of transported molecules as a function of distance from a population of TN-forming cells. Our model predicts how the perfusion of molecules through the TNs is affected by the size of the transferred molecules, the length and stability of nanotube formation, and the differences between membrane-bound and cytosolic proteins. To our knowledge, this is the first published mathematical model of intercellular transfer through tunneling nanotubes. We envision that experimental observations will be able to confirm or improve the assumptions made in our model. Furthermore, quantifying the form of inter-cellular communication in the basic scenario envisioned in our model can help suggest ways to measure and investigate cases of possible regulation of either formation of tunneling nanotubes or transport through them.
The next problem we focus on is uncovering how the interactions between the genes and proteins in a cell organize into pathways to process call signals or perform other tasks. The ability to accurately model and deeply understand gene and protein interaction networks of various kinds can be very powerful for prioritizing candidate genes and predicting their role in various signaling pathways and processes. A popular technique for gene prioritization and function prediction is the graph diffusion kernel. We show how the graph diffusion kernel is mathematically similar to the Ising spin graph, a model popular in statistical physics but not usually employed on biological interaction networks. We develop a new method for calculating gene association based on the Ising spin model which is different from the methods common in either bioinformatics or statistical physics. We show that our method performs better than both the graph diffusion kernel and its commonly used equivalent in the Ising model. We present a theoretical argument for understanding its performance based on ideas of phase transitions on networks. We measure its performance by applying our method to link prediction on protein interaction networks. Unlike candidate gene prioritization or function prediction, link prediction does not depend on the existing annotation or characterization of genes for ground truth. It helps us to avoid the confounding noise and uncertainty in the network and annotation data. As a purely network analysis problem, it is well suited for comparing network analysis methods. Once we know that we are accurately modeling the interaction network, we can employ our model to solve other problems like gene prioritization using interaction data.
We also apply statistical analysis for a specific instance of a cell signaling process: the drought response in Brassica napus, a plant of scientific and economic importance. Important changes in the cell physiology of guard cells are initiated by abscisic acid, an important phytohormone that signals water deficit stress. We analyse RNA-seq reads resulting from the sequencing of mRNA extracted from protoplasts treated with abscisic acid. We employ sequence analysis, statisitical modeling, and the integration of cross-species network data to uncover genes, pathways, and interactions important in this process. We confirm what is known from other species and generate new gene and interaction candidates. By associating functional and sequence modification, we are also able to uncover evidence of evolution of gene specialization, a process that is likely widespread in polyploid genomes.
This work has developed new computational methods and applied existing tools for understanding cellular signaling and pathways. We have applied statistical analysis to integrate expression, interactome, pathway, regulatory elements, and homology data to infer \textit{Brassica napus} genes and their roles involved in drought response. Previous literature suggesting support for our findings from other species based on independent experiments is found for many of of these findings. By relating the changes in regulatory elements, our RNA-seq results and common gene ancestry, we present evidence of its evolution in the context of polyploidy. Our work can provide a scientific basis for the pursuit of certain genes as targets of breeding and genetic engineering efforts for the development of drought tolerant oil crops. Building on ideas from statistical physics, we developed a new model of gene associations in networks. Using link prediction as a metric for the accuracy of modeling the underlying structure of a real network, we show that our model shows improved performance on real protein interaction networks. Our model of gene associations can be use to prioritize candidate genes for a disease or phenotype of interest. We also develop a mathematical model for a novel inter-cellular mode of biomolecule transfer. We relate hypotheses about the dynamics of TN formation, stability, and nature of molecular transport to quantitative predictions that may be tested by suitable experiments. In summary, this work demostrates the application and development of computational analysis of cell signaling at the level of the transcriptome, the interactome, and physical transport
