Modeling Gene Regulatory Networks from Time Series Data using Particle Filtering

This thesis considers the problem of learning the structure of gene regulatory networks using gene expression time series data. A more realistic scenario where the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter based state estimation algorithm is studied instead of the contemporary linear approximation based approaches. The parameters signifying the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then fed to a LASSO based least squares regression operation, which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with Extended Kalman filtering (EKF), employing Mean Square Error as fidelity criterion using synthetic data and real biological data. Extensive computer simulations illustrate that the particle filter based gene network inference algorithm outperforms EKF and therefore, it can serve as a natural framework for modeling gene regulatory networks

Efficient and Robust Algorithms for Statistical Inference in Gene Regulatory Networks

Inferring gene regulatory networks (GRNs) is of profound importance in the field of computational biology and bioinformatics. Understanding the gene-gene and gene- transcription factor (TF) interactions has the potential of providing an insight into the complex biological processes taking place in cells. High-throughput genomic and proteomic technologies have enabled the collection of large amounts of data in order to quantify the gene expressions and mapping DNA-protein interactions. This dissertation investigates the problem of network component analysis (NCA) which estimates the transcription factor activities (TFAs) and gene-TF interactions by making use of gene expression and Chip-chip data. Closed-form solutions are provided for estimation of TF-gene connectivity matrix which yields advantage over the existing state-of-the-art methods in terms of lower computational complexity and higher consistency. We present an iterative reweighted ℓ2 norm based algorithm to infer the network connectivity when the prior knowledge about the connections is incomplete. We present an NCA algorithm which has the ability to counteract the presence of outliers in the gene expression data and is therefore more robust. Closed-form solutions are derived for the estimation of TFAs and TF-gene interactions and the resulting algorithm is comparable to the fastest algorithms proposed so far with the additional advantages of robustness to outliers and higher reliability in the TFA estimation. Finally, we look at the inference of gene regulatory networks which which essentially resumes to the estimation of only the gene-gene interactions. Gene networks are known to be sparse and therefore an inference algorithm is proposed which imposes a sparsity constraint while estimating the connectivity matrix.The online estimation lowers the computational complexity and provides superior performance in terms of accuracy and scalability. This dissertation presents gene regulatory network inference algorithms which provide computationally efficient solutions in some very crucial scenarios and give advantage over the existing algorithms and therefore provide means to give better understanding of underlying cellular network. Hence, it serves as a building block in the accurate estimation of gene regulatory networks which will pave the way for finding cures to genetic diseases