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A Bayesian approach for parameter estimation in the extended clock gene circuit of Arabidopsis thaliana.

Higham CF, Husmeier D - BMC Bioinformatics (2013)

Bottom Line: The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components.Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection.Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction.

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ABSTRACT
The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.

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Outline of the Arabidopsis circadian clock based on Figure 1 in [4]. The morning and evening loop elements are represented by white and grey boxes respectively. The solid lines indicate transcriptional regulation and the short dashed lines indicate post-translational regulation of TOC1 and EC by GI, ZTL and COP1. An arrow signifies activation and a block inhibition. The EC protein complex formation is denoted by the short-long dashed line. Flashes represent acute light responses and asterisks post-translational regulation by light.
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Figure 1: Outline of the Arabidopsis circadian clock based on Figure 1 in [4]. The morning and evening loop elements are represented by white and grey boxes respectively. The solid lines indicate transcriptional regulation and the short dashed lines indicate post-translational regulation of TOC1 and EC by GI, ZTL and COP1. An arrow signifies activation and a block inhibition. The EC protein complex formation is denoted by the short-long dashed line. Flashes represent acute light responses and asterisks post-translational regulation by light.

Mentions: The circadian clock is a molecular mechansism that synchronises biological processes with the day/night cycle and is found in many organisms [1]. The presence of a clock enables an organism to anticipate and adapt to environmental change and hence use energy sources more efficiently. The mechanism includes interlocked, transcriptional feedback loops. Pokhilko et al. built a mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system [2]. Recent experiments show that three plant-specific proteins ELF3, ELF4 and LUX form an evening complex (EC) which binds to the promoters of target genes [3]. This has led to a revision of the model [4]. The latest version of the clock model, illustrated in Figure 1, represents interconnected morning and evening loops in a three loop structure. The morning loop comprises transcription factors LHY and CCA1, which activate the expression of PRR9 PRR7 and PRR5/NI. The transcriptional co-regulators PRR9, PRR7 and PRR5 inhibit LHY and CCA1 expression by binding to their promoters. The evening loop, previously represented by TOC and a hypothetical gene (Y), introduced by Locke et al. [5] is now represented by TOC, LUX, ELF3 and ELF4.


A Bayesian approach for parameter estimation in the extended clock gene circuit of Arabidopsis thaliana.

Higham CF, Husmeier D - BMC Bioinformatics (2013)

Outline of the Arabidopsis circadian clock based on Figure 1 in [4]. The morning and evening loop elements are represented by white and grey boxes respectively. The solid lines indicate transcriptional regulation and the short dashed lines indicate post-translational regulation of TOC1 and EC by GI, ZTL and COP1. An arrow signifies activation and a block inhibition. The EC protein complex formation is denoted by the short-long dashed line. Flashes represent acute light responses and asterisks post-translational regulation by light.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750527&req=5

Figure 1: Outline of the Arabidopsis circadian clock based on Figure 1 in [4]. The morning and evening loop elements are represented by white and grey boxes respectively. The solid lines indicate transcriptional regulation and the short dashed lines indicate post-translational regulation of TOC1 and EC by GI, ZTL and COP1. An arrow signifies activation and a block inhibition. The EC protein complex formation is denoted by the short-long dashed line. Flashes represent acute light responses and asterisks post-translational regulation by light.
Mentions: The circadian clock is a molecular mechansism that synchronises biological processes with the day/night cycle and is found in many organisms [1]. The presence of a clock enables an organism to anticipate and adapt to environmental change and hence use energy sources more efficiently. The mechanism includes interlocked, transcriptional feedback loops. Pokhilko et al. built a mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system [2]. Recent experiments show that three plant-specific proteins ELF3, ELF4 and LUX form an evening complex (EC) which binds to the promoters of target genes [3]. This has led to a revision of the model [4]. The latest version of the clock model, illustrated in Figure 1, represents interconnected morning and evening loops in a three loop structure. The morning loop comprises transcription factors LHY and CCA1, which activate the expression of PRR9 PRR7 and PRR5/NI. The transcriptional co-regulators PRR9, PRR7 and PRR5 inhibit LHY and CCA1 expression by binding to their promoters. The evening loop, previously represented by TOC and a hypothetical gene (Y), introduced by Locke et al. [5] is now represented by TOC, LUX, ELF3 and ELF4.

Bottom Line: The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components.Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection.Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction.

View Article: PubMed Central - HTML - PubMed

ABSTRACT
The circadian clock is an important molecular mechanism that enables many organisms to anticipate and adapt to environmental change. Pokhilko et al. recently built a deterministic ODE mathematical model of the plant circadian clock in order to understand the behaviour, mechanisms and properties of the system. The model comprises 30 molecular species (genes, mRNAs and proteins) and over 100 parameters. The parameters have been fitted heuristically to available gene expression time series data and the calibrated model has been shown to reproduce the behaviour of the clock components. Ongoing work is extending the clock model to cover downstream effects, in particular metabolism, necessitating further parameter estimation and model selection. This work investigates the challenges facing a full Bayesian treatment of parameter estimation. Using an efficient adaptive MCMC proposed by Haario et al. and working in a high performance computing setting, we quantify the posterior distribution around the proposed parameter values and explore the basin of attraction. We investigate if Bayesian inference is feasible in this high dimensional setting and thoroughly assess convergence and mixing with different statistical diagnostics, to prevent apparent convergence in some domains masking poor mixing in others.

Show MeSH
Related in: MedlinePlus