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A framework for modelling gene regulation which accommodates non-equilibrium mechanisms.

Ahsendorf T, Wong F, Eils R, Gunawardena J - BMC Biol. (2014)

Bottom Line: At equilibrium, microstate probabilities do not depend on how a microstate is reached but, away from equilibrium, each path to a microstate can contribute to its steady-state probability.Systems that are far from equilibrium thereby become dependent on history and the resulting complexity is a fundamental challenge.As epigenomic data become increasingly available, we anticipate that gene function will come to be represented by graphs, as gene structure has been represented by sequences, and that the methods introduced here will provide a broader foundation for understanding how genes work.

View Article: PubMed Central - PubMed

Affiliation: DKFZ, Heidelberg, D-69120, Germany. tobias.ahsendorf@googlemail.com.

ABSTRACT

Background: Gene regulation has, for the most part, been quantitatively analysed by assuming that regulatory mechanisms operate at thermodynamic equilibrium. This formalism was originally developed to analyse the binding and unbinding of transcription factors from naked DNA in eubacteria. Although widely used, it has made it difficult to understand the role of energy-dissipating, epigenetic mechanisms, such as DNA methylation, nucleosome remodelling and post-translational modification of histones and co-regulators, which act together with transcription factors to regulate gene expression in eukaryotes.

Results: Here, we introduce a graph-based framework that can accommodate non-equilibrium mechanisms. A gene-regulatory system is described as a graph, which specifies the DNA microstates (vertices), the transitions between microstates (edges) and the transition rates (edge labels). The graph yields a stochastic master equation for how microstate probabilities change over time. We show that this framework has broad scope by providing new insights into three very different ad hoc models, of steroid-hormone responsive genes, of inherently bounded chromatin domains and of the yeast PHO5 gene. We find, moreover, surprising complexity in the regulation of PHO5, which has not yet been experimentally explored, and we show that this complexity is an inherent feature of being away from equilibrium. At equilibrium, microstate probabilities do not depend on how a microstate is reached but, away from equilibrium, each path to a microstate can contribute to its steady-state probability. Systems that are far from equilibrium thereby become dependent on history and the resulting complexity is a fundamental challenge. To begin addressing this, we introduce a graph-based concept of independence, which can be applied to sub-systems that are far from equilibrium, and prove that history-dependent complexity can be circumvented when sub-systems operate independently.

Conclusions: As epigenomic data become increasingly available, we anticipate that gene function will come to be represented by graphs, as gene structure has been represented by sequences, and that the methods introduced here will provide a broader foundation for understanding how genes work.

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Microstates and graphs. A fragment of a graph is shown (below), with three vertices, i, j and k, and several labelled, directed edges. Vertex i is expanded into a microstate, or snapshot of a DNA state (above), showing some of the features that can be represented (not to scale). Here, a hypothetical promoter region of a gene is shown. Features include sequence-specific transcription factors bound to DNA (grey shapes), additional recruited components, such as transcriptional co-regulators (orange shapes), general-purpose transcriptional machinery, such as Mediator (yellow), general transcription factors (GTFs, blue-green) and RNA Pol II (magenta), along with chromatin remodellers and enzymatic factors that modify the histone tails of nucleosomes (blue shapes). Potential post-translational modifications of transcription factors, co-regulators and histone tails are shown by the corresponding symbols, along with DNA methylation. Distal enhancers may participate through 3D chromatin conformation, such as DNA looping. CTD is the carboxy terminal domain of RNA Pol II. 3D, three dimensional; CTD, carboxy terminal domain; GTF, general transcription factor; Pol, polymerase; Ac, acetylation; Me, methylation; P, phosphorylation; Ub, ubiquitination.
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Fig1: Microstates and graphs. A fragment of a graph is shown (below), with three vertices, i, j and k, and several labelled, directed edges. Vertex i is expanded into a microstate, or snapshot of a DNA state (above), showing some of the features that can be represented (not to scale). Here, a hypothetical promoter region of a gene is shown. Features include sequence-specific transcription factors bound to DNA (grey shapes), additional recruited components, such as transcriptional co-regulators (orange shapes), general-purpose transcriptional machinery, such as Mediator (yellow), general transcription factors (GTFs, blue-green) and RNA Pol II (magenta), along with chromatin remodellers and enzymatic factors that modify the histone tails of nucleosomes (blue shapes). Potential post-translational modifications of transcription factors, co-regulators and histone tails are shown by the corresponding symbols, along with DNA methylation. Distal enhancers may participate through 3D chromatin conformation, such as DNA looping. CTD is the carboxy terminal domain of RNA Pol II. 3D, three dimensional; CTD, carboxy terminal domain; GTF, general transcription factor; Pol, polymerase; Ac, acetylation; Me, methylation; P, phosphorylation; Ub, ubiquitination.

Mentions: The framework starts with a labelled, directed graph consisting of a collection of vertices with directed edges between pairs of vertices and labels on the edges (Figure 1, bottom). The graphs considered here have only finitely many vertices and the edges always go between distinct vertices, so that there are no self-loops. It is further assumed that each graph is connected, which means that, given any two vertices, there is always a path of edges between them, ignoring edge directions. A connected graph is not in disjoint pieces.Figure 1


A framework for modelling gene regulation which accommodates non-equilibrium mechanisms.

Ahsendorf T, Wong F, Eils R, Gunawardena J - BMC Biol. (2014)

Microstates and graphs. A fragment of a graph is shown (below), with three vertices, i, j and k, and several labelled, directed edges. Vertex i is expanded into a microstate, or snapshot of a DNA state (above), showing some of the features that can be represented (not to scale). Here, a hypothetical promoter region of a gene is shown. Features include sequence-specific transcription factors bound to DNA (grey shapes), additional recruited components, such as transcriptional co-regulators (orange shapes), general-purpose transcriptional machinery, such as Mediator (yellow), general transcription factors (GTFs, blue-green) and RNA Pol II (magenta), along with chromatin remodellers and enzymatic factors that modify the histone tails of nucleosomes (blue shapes). Potential post-translational modifications of transcription factors, co-regulators and histone tails are shown by the corresponding symbols, along with DNA methylation. Distal enhancers may participate through 3D chromatin conformation, such as DNA looping. CTD is the carboxy terminal domain of RNA Pol II. 3D, three dimensional; CTD, carboxy terminal domain; GTF, general transcription factor; Pol, polymerase; Ac, acetylation; Me, methylation; P, phosphorylation; Ub, ubiquitination.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4288563&req=5

Fig1: Microstates and graphs. A fragment of a graph is shown (below), with three vertices, i, j and k, and several labelled, directed edges. Vertex i is expanded into a microstate, or snapshot of a DNA state (above), showing some of the features that can be represented (not to scale). Here, a hypothetical promoter region of a gene is shown. Features include sequence-specific transcription factors bound to DNA (grey shapes), additional recruited components, such as transcriptional co-regulators (orange shapes), general-purpose transcriptional machinery, such as Mediator (yellow), general transcription factors (GTFs, blue-green) and RNA Pol II (magenta), along with chromatin remodellers and enzymatic factors that modify the histone tails of nucleosomes (blue shapes). Potential post-translational modifications of transcription factors, co-regulators and histone tails are shown by the corresponding symbols, along with DNA methylation. Distal enhancers may participate through 3D chromatin conformation, such as DNA looping. CTD is the carboxy terminal domain of RNA Pol II. 3D, three dimensional; CTD, carboxy terminal domain; GTF, general transcription factor; Pol, polymerase; Ac, acetylation; Me, methylation; P, phosphorylation; Ub, ubiquitination.
Mentions: The framework starts with a labelled, directed graph consisting of a collection of vertices with directed edges between pairs of vertices and labels on the edges (Figure 1, bottom). The graphs considered here have only finitely many vertices and the edges always go between distinct vertices, so that there are no self-loops. It is further assumed that each graph is connected, which means that, given any two vertices, there is always a path of edges between them, ignoring edge directions. A connected graph is not in disjoint pieces.Figure 1

Bottom Line: At equilibrium, microstate probabilities do not depend on how a microstate is reached but, away from equilibrium, each path to a microstate can contribute to its steady-state probability.Systems that are far from equilibrium thereby become dependent on history and the resulting complexity is a fundamental challenge.As epigenomic data become increasingly available, we anticipate that gene function will come to be represented by graphs, as gene structure has been represented by sequences, and that the methods introduced here will provide a broader foundation for understanding how genes work.

View Article: PubMed Central - PubMed

Affiliation: DKFZ, Heidelberg, D-69120, Germany. tobias.ahsendorf@googlemail.com.

ABSTRACT

Background: Gene regulation has, for the most part, been quantitatively analysed by assuming that regulatory mechanisms operate at thermodynamic equilibrium. This formalism was originally developed to analyse the binding and unbinding of transcription factors from naked DNA in eubacteria. Although widely used, it has made it difficult to understand the role of energy-dissipating, epigenetic mechanisms, such as DNA methylation, nucleosome remodelling and post-translational modification of histones and co-regulators, which act together with transcription factors to regulate gene expression in eukaryotes.

Results: Here, we introduce a graph-based framework that can accommodate non-equilibrium mechanisms. A gene-regulatory system is described as a graph, which specifies the DNA microstates (vertices), the transitions between microstates (edges) and the transition rates (edge labels). The graph yields a stochastic master equation for how microstate probabilities change over time. We show that this framework has broad scope by providing new insights into three very different ad hoc models, of steroid-hormone responsive genes, of inherently bounded chromatin domains and of the yeast PHO5 gene. We find, moreover, surprising complexity in the regulation of PHO5, which has not yet been experimentally explored, and we show that this complexity is an inherent feature of being away from equilibrium. At equilibrium, microstate probabilities do not depend on how a microstate is reached but, away from equilibrium, each path to a microstate can contribute to its steady-state probability. Systems that are far from equilibrium thereby become dependent on history and the resulting complexity is a fundamental challenge. To begin addressing this, we introduce a graph-based concept of independence, which can be applied to sub-systems that are far from equilibrium, and prove that history-dependent complexity can be circumvented when sub-systems operate independently.

Conclusions: As epigenomic data become increasingly available, we anticipate that gene function will come to be represented by graphs, as gene structure has been represented by sequences, and that the methods introduced here will provide a broader foundation for understanding how genes work.

Show MeSH