Analysis Of Genotype-phenotype Related Problems By Statistical Genetics And Computational Biology

My thesis includes two major research topics, and tries to investigate some problems about the genetype-phenotype mapping from two different levels. The first one is to study the estimation problem of pleiotropy using statistical model in a large scale level. Gene pleiotropy is the capability of a gene affecting multiple phenotypes. We estimate pleiotropy from protein sequence data without counting the effected phenotypes that usually unknown. The second one is to explore the nonlinear dynamic problems about one specific genetype-phenotype mapping from microscope level. We formulate a mathematical framework for exploring the regulation mechanism of exocytotic membrane fusion to understand mechanistically how the underlying biochemical pathways determine the up-level cellular behaviors. The long-term goal of my work is to develop an integrated mathematical framework to have a better understanding of the complexity of biological systems.In the first research topic, we are focusing on the problem of gene pleiotropy, which has played a central role in genetics, development and evolution. Though in recent years functional genomics in model organisms has brought high throughput data to bear on the nature and extent of pleiotropy, the nature and extent of gene pleiotropy remains highly controversial. Meanwhile, an avenue of new research has emerged in attempt to estimate pleiotropy from the genetics data without counting the number of affected phenotypes. Gu developed a statistical method to estimate the ’effective pleiotropy’of a gene based on the multiple sequence alignment of protein sequences without counting phenotypes. In spite of extensive discussions, the biological interpretation is still not very clear. To solve this problem, we first formulate the theory of minimum pleiotropy that is connected to the rank of genotype-fitness map, i.e., the number of distinct mapping lines from genotype to fitness (molecular phenotypes). Secondly, we show that Gu actually estimated the rank of genotype-phenotype mapping, which can be used as an effective estimate for the degree of gene pleiotropy under certain conditions. Moreover, we used both real datasets and computer simulations and the results support the predictions of this theory. Moreover, we develop a new method to correct the estimation method bias in the original work.In the second topic, we propose a framework for exploring the regulation mechanism of exocytotic membrane fusion. One difficulty in conducting biologically meaningful dynamic analysis at the systems biology level is that in vivo system regulation is complex. Meanwhile, as many kinetic rates are unknown, global system analysis is intractable in practice. In this article, we demonstrate a computational pipeline to help solve this problem, using the exocytotic process as an example. Exocytosis is an essential process in all eukaryotic cells that allows communication in cells through vesicles that contain a wide range of intracellular molecules. During this process a set of proteins called SNAREs acts as an engine in this vesicle-membrane fusion, by forming four-helical bundle complex between (membrane) target-specific and vesicle-specific SNAREs. As expected, the regulatory network for exocytosis is very complex. Based on the current understanding of the protein-protein interaction network related to exocytosis, we mathematically formulated the whole system, by the ordinary differential equations (ODE). We then applied a mathematical approach (called inverse problem) to estimating the kinetic parameters in the fundamental subsystem (without regulation) from limited in vitro experimental data, which fit well with the reports by the conventional assay. These estimates allowed us to conduct an efficient stability analysis under a specified parameter space for the exocytotic process with or without regulation. Finally, we discuss the potential of this approach to explain experimental observations and to make testable hypotheses for further experimentation.