Mathematical models play an important role in the design of synthetic gene circuits, by guiding the choice of biological components and their assembly into novel gene networks. Here, we present a guide for biologists ...
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Mathematical models play an important role in the design of synthetic gene circuits, by guiding the choice of biological components and their assembly into novel gene networks. Here, we present a guide for biologists to build and utilize models of gene networks (synthetic or natural) to analyze dynamical properties of these networks while considering the low numbers of molecules inside cells that results in stochastic gene expression. We start by describing how to write down a model and discussing the level of details to include. We then briefly demonstrate how to simulate a network’s dynamics using deterministic differential equations that assume high numbers of molecules. To consider the role of stochastic gene expression in single cells, we provide a detailed tutorial on running stochastic gillespie simulations of a network, including instructions on coding the gillespie algorithm with example code. Finally, we illustrate how using a combination of quantitative experimental characterization of a synthetic circuit and mathematical modeling can guide the iterative redesign of a synthetic circuit to achieve the desired properties. This is shown using a classic synthetic oscillator, the repressilator, which we recently redesigned into the most precise and robust synthetic oscillator to date. We thus provide a toolkit for synthetic biologists to build more precise and robust synthetic circuits, which should lead to a deeper understanding of the dynamics of gene regulatory networks. less
The maintenance of transcriptional states regulated by histone modifications and controlled switching between these states are fundamental concepts in our understanding of nucleosome-mediated epigenetic memory. Any ap...
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The maintenance of transcriptional states regulated by histone modifications and controlled switching between these states are fundamental concepts in our understanding of nucleosome-mediated epigenetic memory. Any approach relying on genome-wide bioinformatic analyses alone offers limited scope for dissecting the molecular mechanisms involved in maintenance and switching. Mechanistic mathematical models—describing the dynamics of histone modifications at individual genomic loci—offer an alternative way to investigate these mechanisms. These models, in conjunction with quantitative experimental data—ChIP data, quantification of mRNA levels, and single-cell fluorescence tracking in clonal lineages—can generate predictions that drive more targeted experiments, allowing us to understand mechanisms that would be challenging to unravel by a purely experimental approach. In this chapter, we describe a generic stochastic modeling framework that can be used to capture histone modification dynamics and associated molecular processes—including transcription and read–write feedback by chromatin modifying complexes—at individual genomic loci. Using a specific example—transcriptional silencing by Polycomb-mediated H3K27 methylation—we demonstrate how to construct and simulate a stochastic histone modification model. We provide a step-by-step guide to programming simulations for such a model and discuss how to analyze the simulation output. less
Background: The steady-state behaviour of gene regulatory networks (GRNs) can provide crucial evidence for detecting disease-causing genes. However, monitoring the dynamics of GRNs is particularly difficult because bi...
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