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Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This…

Regulatory interactions between genes show a large amount of cross-species variability, even when the underlying functions are conserved: There are many ways to achieve the same function. Here we investigate the ability of regulatory…

Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…

Regulatory networks describe the interactions between molecular or cellular regulators, like transcription factors and genes in gene regulatory networks, kinases and their receptors in signalling networks, or neurons in neural networks. A…

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…

Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…

Gene regulatory networks are collections of genes that interact with one other and with other substances in the cell. By measuring gene expression over time using high-throughput technologies, it may be possible to reverse engineer, or…

Modelling gene regulatory networks not only requires a thorough understanding of the biological system depicted but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to…

Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is of fundamental importance for the study of single-cell stochastic gene expression. Here by solving the…

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…

Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or…

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. What mechanisms might be responsible for these low in-degrees? Starting with an accepted framework of the…

Genetic Regulatory Networks (GRNs) plays a vital role in the understanding of complex biological processes. Modeling GRNs is significantly important in order to reveal fundamental cellular processes, examine gene functions and understanding…

We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In…

The structure of a stochastic nonlinear gene regulatory network is uncovered by studying its response to input signal generators. Four applications are studied in detail: a nonlinear connection of two linear systems, the design of a logic…

Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. We here analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation…

Genetic regulatory networks enable cells to respond to the changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits…

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these…

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean…