Computational approaches for modeling intrinsic noise and delays in genetic regulatory networks

This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a molecular biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003; Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004; Horikawa et al., 2006)

Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches

Modeling intrinsic noise and delays in chemical kinetics of coupled autoregulated oscillating cells

Delays are an important feature in temporal models of genetic regulation due to slow biochemical processes, such as transcription and translation. In this paper, we show how to model intrinsic noise effects in a delayed setting by either using a delay stochastic simulation algorithm (DSSA) or, for larger and more complex systems, a generalized Binomial τ-leap method (Bτ-DSSA). As a particular application, we apply these ideas to modeling somite segmentation in zebra fish across a number of cells in which two linked oscillatory genes (her1 and her7) are synchronized via Notch signaling between the cells

A review of stochastic and delay simulation approaches in both time and space in computational cell biology

Heterogeneity and variability is ubiquitous in biology and physiology and one of the great modelling challenges is how we cope with and quantify this variability. There are a wide variety of approaches. We can attempt to ignore spatial effects and represent the heterogeneity through stochastic models that evolve only in time, or we can attempt to capture some key spatial components. Alternatively we can perform very detailed spatial simulations or we can attempt to use other approaches that mimic stochasticity in some way, such as by the use of delay models, or by using populations of deterministic models. The skill is knowing when a particular model is appropriate to the questions that are being addressed. In this review, we give a brief introduction to modelling and simulation in Computational Biology and discuss the various different sources of heterogeneity, pointing out useful modelling and analysis approaches. The starting point is how we deal with intrinsic noise; that is, the uncertainty of knowing when a chemical reaction takes place and which that reaction is. These discrete stochastic methods do not follow individual molecules over time; rather they track only total molecular numbers. This leads, in the first instance, to the Stochastic Simulation Algorithm that describes the time evolution of a discrete nonlinear Markov process. From there we consider approaches that are more efficient and effective but still preserve the discreteness of the simulation, so-called tau-leaping algorithms. We then move to approximations that are continuous in time based around the Chemical Langevin stochastic differential equation. In these contexts we will focus, later in this chapter, on a particular application, namely the behaviour of ion channels dynamics. In the second part of the review, we address the question of spatial heterogeneity. This involves consideration on the nature of diffusion in crowded spaces and, in particular, anomalous diffusion, a relevant topic (for example) in the analysis and simulation of cell membrane dynamics. We discuss different approaches for capturing this spatial heterogeneity through generalisations of the Stochastic Simulation Algorithm and that eventually leads us to the concept of fractional differential equations. Finally we consider the use of delays in capturing stochastic effects. For each case we attempt to give a discussion of applicable methods and an indication of their advantages and disadvantages

Modelling and simulation techniques for membrane biology

One of the most important aspects of Computational Cell Biology is the understanding of the complicated dynamical processes that take place on plasma membranes. These processes are often so complicated that purely temporal models cannot always adequately capture the dynamics.On the other hand, spatial models can have large computational overheads. In this article, we review some of these issues with respect to chemistry, membrane microdomains and anomalous diffusion and discuss how to select appropriate modelling and simulation paradigms based on some or all the following aspects: discrete, continuous, stochastic, delayed and complex spatial processes