Traditionally molecular biology research has tended to reduce biological pathways to composite units studied as isolated parts of the cellular system. With the advent of high throughput methodologies that can capture thousands of data points, and powerful computational approaches, the reality of studying cellular processes at a systems level is upon us. As these approaches yield massive datasets, systems level analyses have drawn upon other fields such as engineering and mathematics, adapting computational and statistical approaches to decipher relationships between molecules. Guided by high quality datasets and analyses, one can begin the process of predictive modeling. The findings from such approaches are often surprising and beyond normal intuition. We discuss four classes of dynamical systems used to model genetic regulatory networks. The discussion is divided into continuous and discrete models, as well as deterministic and stochastic model classes. For each combination of these categories, a model is presented and discussed in the context of the yeast cell cycle, illustrating how different types of questions can be addressed by different model classes.

When living systems detect changes in their external environment their response must be measured to balance the need to react appropriately with the need to remain stable, ignoring insignificant signals. Because this is a fundamental challenge of all biological systems that execute programs in response to stimuli, we developed a generalized time-frequency analysis (TFA) framework to systematically explore the dynamical properties of biomolecular networks. Using TFA, we focused on two well-characterized yeast gene regulatory networks responsive to carbon-source shifts and a mammalian innate immune regulatory network responsive to lipopolysaccharides (LPS). The networks are comprised of two different basic architectures. Dual positive and negative feedback loops make up the yeast galactose network; whereas overlapping positive and negative feed-forward loops are common to the yeast fatty-acid response network and the LPS-induced network of macrophages. TFA revealed remarkably distinct network behaviors in terms of trade-offs in responsiveness and noise suppression that are appropriately tuned to each biological response. The wild type galactose network was found to be highly responsive while the oleate network has greater noise suppression ability. The LPS network appeared more balanced, exhibiting less bias toward noise suppression or responsiveness. Exploration of the network parameter space exposed dramatic differences in system behaviors for each network. These studies highlight fundamental structural and dynamical principles that underlie each network, reveal constrained parameters of positive and negative feedback and feed-forward strengths that tune the networks appropriately for their respective biological roles, and demonstrate the general utility of the TFA approach for systems and synthetic biology.

Author Summary

Biological systems constantly balance noise suppression with responsiveness. In a fluctuating environment, some changes are insignificant to living cells while others represent cues to which they must respond. These stimuli are interpreted by molecular circuits that enable the cell to strike an appropriate balance between responsiveness and noise suppression. This trade-off is governed by the structure and kinetic parameters of molecular networks, which have been tuned by evolutionary selection for different stimuli and responses. We consider three regulatory circuits (two from yeast and one from mammalian cells), which respond to different environments and involve very different physiological processes. To investigate the responses to a time varying signal, we developed a generalized time-frequency analysis framework for studying such trade-offs using mathematical models of regulatory circuits and explore how the structure and parameters of the circuit affect the trade-offs between noise suppression and responsiveness. The generalized TFA approach represents an effective tool for exploring and analyzing different systems-level dynamical properties. Making use of such properties can facilitate prediction and network control for systems- and synthetic biology applications.

Peroxisomes are intracellular organelles that house a number of diverse metabolic processes, notably those required for β-oxidation of fatty acids. Peroxisomes biogenesis can be induced by the presence of peroxisome proliferators, including fatty acids, which activate complex cellular programs that underlie the induction process. Here, we used multi-parameter quantitative phenotype analyses of an arrayed mutant collection of yeast cells induced to proliferate peroxisomes, to establish a comprehensive inventory of genes required for peroxisome induction and function. The assays employed include growth in the presence of fatty acids, and confocal imaging and flow cytometry through the induction process. In addition to the classical phenotypes associated with loss of peroxisomal functions, these studies identified 169 genes required for robust signaling, transcription, normal peroxisomal development and morphologies, and transmission of peroxisomes to daughter cells. These gene products are localized throughout the cell, and many have indirect connections to peroxisome function. By integration with extant data sets, we present a total of 211 genes linked to peroxisome biogenesis and highlight the complex networks through which information flows during peroxisome biogenesis and function.