State-Space Model with Time Delays for Genetic Regulatory Networks
Fang-Xiang Wu, Wen-Jun Zhang, and Anthony J. Kusalik
University of Saskatchewan

A living cell can be considered a dynamic system (called a cellular system) in which the behaviour (development) of the cell depends completely on the current internal state plus any external inputs, if these exist. Although many details inside a cell are not precisely known, gene expression data on a genome scale provides useful insights into such a cellular system. With gene expression data, a wide variety of models, such as Boolean networks and differentia/difference equations, have been introduced to model cellular systems. In these previously proposed models, genes were viewed as the internal state variables of a cellular system. This viewpoint has suffered from the under-estimation of the model parameters. In addition, these models ignore an important problem with a cellular system time delay. Instead, we view genes as the observation variables, whose expression values depend on the current internal state variables and any external inputs. Bayesian information criterion (BIC) and probabilistic principal component analysis (PPCA) are used to estimate the number of the internal state variables and their expression profiles from gene expression data. By constructing dynamic equations with time delays for the internal state variables and the relationships between the internal state variables and the observation variables (gene expression profiles), state-space models with time delays for genetic regulatory networks are realized. In the method present, model parameters may be unambiguously identified from time-course gene expression data with cheap computational cost. The method is applied to two time-course gene expression datasets, and two models constructed. The models are (almost) stable. Further, compared to models without incorporating time delay, our model has better prediction accuracy.

Nonlinear Modeling on Protein Kinase C(PKC)-ε Negative Regulation of Stress Fibers in Oncogenically Transformed Cells
Yingxin Li, Carol Heckman, and Julie Barnes
Dept. of Computer Science, Bowling Green State University

Phorbol 12-myristate 13-acetate (PMA), a tumor promoter, provides an effective means of reversibly converting tissue culture cells to a state which resembles that of transformed cells. PMA is known to activate PKC and cause reorganization of actin-containing structures. The purpose of the current research is to analyze the pattern in which PKC mediates dissolution of stress fibers (SFs) by a mathematical model. Upon PMA exposure, rat tracheal 1000 W cells showed stress fiber formation and down regulation of PKC-ε in the time period from 5 to 10 hours. Several mathematical models were tried, including linear and nonlinear approximations, in order to establish the relationship between PKC-ε and SF accumulation in 1000W cells. Applying a non-linear approximation and using a bisection algorithm, an exponential function was derived to show how PKC-ε negatively controlled SFs. The SF-forming cells followed the function: F(x)= 0.6833* e0.8412(x- 0.387), where F is the percentage of SF-forming cells and x is the content of PKC-ε. To further validate this mathematical model, RNA interference (RNAi) technology was applied to knock down the PKC-ε expression. Analysis of the time course of SF formation following PMA exposure of cells after introduction of siRNA, suggested that PKC-ε might bind with actin or actin-binding protein and, by phosphorylating a protein integral to their structure, mediate SF dissolution.

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Analysis of Population Dynamics in Beta-cell Destruction Lead to Identification of Novel Candidate Genes for Type 1 Diabetes
Yizhou Xie and Xujing Wang
Medical College of Wisconsin

Type 1 diabetes (T1D) results from the immune destruction of the insulin-producing beta cells. Like many other complex disease, where the exact disease etiology is still unclear, a major difficulty in its genetic study is the lack of means to identify candidate disease genes. We have developed a minimal model for T1D where we mathematically formulate the population dynamics for the most critical components in b-cell destruction: macrophages, T lymphocytes, beta cells and beta-cell autoantigens. We investigate the consequence of an elevated wave of beta cell apoptosis (which resembles the initiation of disease) to the system dynamic stability, and thus identify the key factors that lead to or protect against a disease process. All major findings are consistent with clinical/laboratory data. Specifically, the model revealed that adult disease susceptibility is critically determined by 4 major pathways: (1) b-cell autoantigen release, (2) cytokine induced b-cell death, (3) phagocytosis, and (4) macrophage activation. Together they provide a comprehensive picture of where the candidate genes most likely lie. We will present our mathematical model, our bioinformatics platform to retrieve and update the gene information involved in these pathways, and our candidate gene database. In addition we will present our study design to genotype the candidate genes, in the largest patient sample collection that we have. Our innovative approach integrates bioinformatics and mathematical modeling with genetic study. As far as we are aware, it represents the first time understanding the disease dynamics is combined with the genetic study of a complex disease.

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