Dynamic model and its applications to molecular and physiological data analysis

Lerong Li, The University of Texas School of Public Health


An important goal for classifying dynamic and functional data is to determine how to effectively reduce their dimension while exploring dynamic features. However, few statistical methods for dynamic data classification have directly used rich dynamic data features. To overcome this limitation, we proposed a novel approach for QRS complex classification based on second order ordinary differential equation (ODE), which combines morphological and dynamic feature of highly correlated QRS complex. We developed a method based on principal differential analysis to estimate constant or time-varying parameters in the ODE. We used the parameters in the ODE as features for classifiers. The proposed method was validated on the MIT-BIH arrhythmia database. We showed that the ODE-based classification methods in QRS complex classification can outperform the currently widely used neural networks with Fourier expansion coefficients of the functional data as their features. ^ Characterizing gene regulation and capturing important features will provide valuable information for understanding biological process. Variation in gene expression underlies many biological processes and holds a key to unraveling mechanism of gene regulation. To unravel the features of gene transcription, we proposed to use a differential equation to model the observed number of reads across the gene. We took the number of reads as a function of the genomic position, and viewed the transcription process as a dynamic process of transcription along the genome. We developed a location-varying dynamic model for the dynamics of transcription processes along the genome. This proposed model was applied to Kidney Renal Clear Cell Carcinoma (KIRC) RNA-seq data with 72 matched pair of KIRC and normal samples from TCGA datasets. We studied the stability and transient response of transcriptional processes for each gene using a fitted differential equation. We used the coefficients of ODE to classify the gene transcriptions with similar pattern. We also identified genes that showed significantly differential dynamic behaviors as a response to environmental perturbation. ^ The brain is organized into anatomically distinct functional regions that are connected by the activation of neural networks over time and interactions between activated brain areas are measured indirectly and are therefore estimated. Historically, the multivariate autoregressive model (MVAR) has been used to describe the temporal patterns of brain activity and Granger Causality concepts have been used as important tools for estimating interactions between neuronal regions. However, the MVAR-based methodologies are limited as they require signals from brain activity to be stationary and also demand heavy computation. To overcome these limitations, the state-space equations and linear Kalman Filter was recently proposed to estimate functional connectivity between brain regions. Alternative to the Kalman Filter approach, we proposed to use system of differential equations to map brain functional connectivity. We therefore developed a functional data analysis method to estimate the parameters in a system of differential equations.^

Subject Area

Biology, Biostatistics|Biology, Bioinformatics

Recommended Citation

Li, Lerong, "Dynamic model and its applications to molecular and physiological data analysis" (2014). Texas Medical Center Dissertations (via ProQuest). AAI3689779.