## Modeling Nonlinear Behavior of Dynamic Biological Systems

- Author(s): Masnadi-Shirazi, Maryam
- Advisor(s): Subramaniam, Shankar
- Cosman, Pamela
- et al.

## Abstract

With the availability of large-scale data acquired through high-throughput technologies, computational systems biology has made substantial progress towards partially modeling biological systems. In this dissertation we intend to focus on deciphering the dynamics of such systems through data-driven analysis of multivariate time-course data. We develop integrative frameworks to study the following problems: 1) time-varying causal inference when the number of samples exceeds the number of variables (overdetermined case), 2) dynamic causal network reconstruction when the number of variables exceeds the data samples (underdetermined case), 3) forecasting the dynamic behavior of complex chaotic systems from short and noisy time-series

data. In the first scenario we utilize the notion of Granger causality identified by a first-order vector autoregressive (VAR) model on phosphoproteomic measurements to unravel the crosstalk between various phosphoproteins in three distinct time intervals. In scenario 2 we use a non-parametric change point detection (CPD) algorithm on transcriptional time series data from a mouse cell cycle to estimate temporal patterns that can be associated with different phases of the cell cycle. In the second scenario the problem becomes more complex as the number of variables exceeds the number of time-series data and we use a higher order VAR models to estimate causal interactions among cell cycle genes. To solve this ill-posed problem we use Least Absolute Shrinkage and Selection Operator (LASSO) and select the regularization parameters through Estimation Stability with Cross Validation (ES-CV) leading to more biologically meaningful results. LASSO + ES-CV is applied to temporal intervals associated with the G1, S and G2/M phases of the cell cycle to estimate phase-specific intracellular interactions. In problem 3, we develop a nonparametric forecasting algorithm for chaotic dynamic systems, Multiview Radial Basis Function Network (MV-RBFN) that outperforms a model-free approach, Multiview Embedding (MVE). In this algorithm, the forecast skill of all possible manifolds (views) reconstructed from a combination of variables and their time lags is assessed and ranked from best to worst. MV-RBFN uses the top k views as the inputs of a neural network to approximate a nonlinear function f(.) that maps the past events of a dynamic system as the input, to future values as the output.