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Modelling nonstationary gene regulatory processes.

Grzegorcyzk M, Husmeier D, Rahnenführer J - Adv Bioinformatics (2010)

Bottom Line: The former aim to relax the homogeneity assumption, whereas the latter are more flexible and, in principle, more adequate for modelling nonlinear processes.In our paper, we compare both paradigms and discuss theoretical shortcomings of the latter approach.We show that a model based on the changepoint process yields systematically better results than the free allocation model when inferring nonstationary gene regulatory processes from simulated gene expression time series.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, TU Dortmund University, 44221 Dortmund, Germany.

ABSTRACT
An important objective in systems biology is to infer gene regulatory networks from postgenomic data, and dynamic Bayesian networks have been widely applied as a popular tool to this end. The standard approach for nondiscretised data is restricted to a linear model and a homogeneous Markov chain. Recently, various generalisations based on changepoint processes and free allocation mixture models have been proposed. The former aim to relax the homogeneity assumption, whereas the latter are more flexible and, in principle, more adequate for modelling nonlinear processes. In our paper, we compare both paradigms and discuss theoretical shortcomings of the latter approach. We show that a model based on the changepoint process yields systematically better results than the free allocation model when inferring nonstationary gene regulatory processes from simulated gene expression time series. We further cross-compare the performance of both models on three biological systems: macrophages challenged with viral infection, circadian regulation in Arabidopsis thaliana, and morphogenesis in Drosophila melanogaster.

No MeSH data available.


Related in: MedlinePlus

Heat maps—macrophages data. Graphical heat map presentation of the temporal connectivity structure for the macrophage gene expression time series. (a), (b), and (c): Heat matrices for experiments CMV (a), IFNGγ (b), and CMV+IFNγ (c) inferred with the BGM model. (d), (e), and (f): Heat matrices for experiments CMV (d), IFNGγ (e), and CMV+IFNγ (f) inferred with the novel BGMD model. Each heat map indicates the estimated posterior probability of two time points being assigned to the same compartment (mixture component). The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0. The numbers on the axes represent the time points of the time course experiment.
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fig3: Heat maps—macrophages data. Graphical heat map presentation of the temporal connectivity structure for the macrophage gene expression time series. (a), (b), and (c): Heat matrices for experiments CMV (a), IFNGγ (b), and CMV+IFNγ (c) inferred with the BGM model. (d), (e), and (f): Heat matrices for experiments CMV (d), IFNGγ (e), and CMV+IFNγ (f) inferred with the novel BGMD model. Each heat map indicates the estimated posterior probability of two time points being assigned to the same compartment (mixture component). The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0. The numbers on the axes represent the time points of the time course experiment.

Mentions: For the macrophages data the BGM model inferred a biologically plausible state change in the host macrophage brought about by infection (CMV) or immune activation (IFNγ), and a less pronounced state change in the combined condition CMV+IFNγ [4]. We compare these findings with results obtained with the novel BGMD model. The fraction of sampled states for which two time points ti and tj are allocated to the same component k (1 ≤ k ≤ K) can be used as a connectivity measure C(ti, tj), and the resulting temporal connectivity structures are displayed graphically as heat maps in Figure 3. All six heatmaps in Figure 3 reflect the two-stage nature of the gene-regulatory processes in the host macrophages: the first part (time points (t2,…, t6)) and the last part of the three time series (time points (t7,…, t25)) are allocated to different components. For all three conditions, a stronger separation between the two regulatory states is inferred by the BGMD model (see Figures 3(d), 3(e), and 3(f)). It appears that the BGMD inference results are more consistent, as even for the combined condition (CMV+IFNγ) a clear trend towards a dichotomous regulatory process can be found (see Figure 3(d)). This finding (stronger separation) is consistent with our conjecture that the novel BGMD assigns neighbouring time-points to the same compartment more likely a priori. Interestingly, the BGM inference outlier at time point t9 in Figure 3(b) yields a certain trend for a subdivision of the second compartment (t7,…, t25) by the BGMD model. Instead of one outlying time point two substages (t7,…, t10) and (t11,…, t25) are inferred (see Figure 3(e)). To provide statistical evidence that the new BGMD model does not overfit the data, we compute predictive probabilities for the BGMD model and compare them with those reported for the BGM model [4].


Modelling nonstationary gene regulatory processes.

Grzegorcyzk M, Husmeier D, Rahnenführer J - Adv Bioinformatics (2010)

Heat maps—macrophages data. Graphical heat map presentation of the temporal connectivity structure for the macrophage gene expression time series. (a), (b), and (c): Heat matrices for experiments CMV (a), IFNGγ (b), and CMV+IFNγ (c) inferred with the BGM model. (d), (e), and (f): Heat matrices for experiments CMV (d), IFNGγ (e), and CMV+IFNγ (f) inferred with the novel BGMD model. Each heat map indicates the estimated posterior probability of two time points being assigned to the same compartment (mixture component). The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0. The numbers on the axes represent the time points of the time course experiment.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2913537&req=5

fig3: Heat maps—macrophages data. Graphical heat map presentation of the temporal connectivity structure for the macrophage gene expression time series. (a), (b), and (c): Heat matrices for experiments CMV (a), IFNGγ (b), and CMV+IFNγ (c) inferred with the BGM model. (d), (e), and (f): Heat matrices for experiments CMV (d), IFNGγ (e), and CMV+IFNγ (f) inferred with the novel BGMD model. Each heat map indicates the estimated posterior probability of two time points being assigned to the same compartment (mixture component). The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0. The numbers on the axes represent the time points of the time course experiment.
Mentions: For the macrophages data the BGM model inferred a biologically plausible state change in the host macrophage brought about by infection (CMV) or immune activation (IFNγ), and a less pronounced state change in the combined condition CMV+IFNγ [4]. We compare these findings with results obtained with the novel BGMD model. The fraction of sampled states for which two time points ti and tj are allocated to the same component k (1 ≤ k ≤ K) can be used as a connectivity measure C(ti, tj), and the resulting temporal connectivity structures are displayed graphically as heat maps in Figure 3. All six heatmaps in Figure 3 reflect the two-stage nature of the gene-regulatory processes in the host macrophages: the first part (time points (t2,…, t6)) and the last part of the three time series (time points (t7,…, t25)) are allocated to different components. For all three conditions, a stronger separation between the two regulatory states is inferred by the BGMD model (see Figures 3(d), 3(e), and 3(f)). It appears that the BGMD inference results are more consistent, as even for the combined condition (CMV+IFNγ) a clear trend towards a dichotomous regulatory process can be found (see Figure 3(d)). This finding (stronger separation) is consistent with our conjecture that the novel BGMD assigns neighbouring time-points to the same compartment more likely a priori. Interestingly, the BGM inference outlier at time point t9 in Figure 3(b) yields a certain trend for a subdivision of the second compartment (t7,…, t25) by the BGMD model. Instead of one outlying time point two substages (t7,…, t10) and (t11,…, t25) are inferred (see Figure 3(e)). To provide statistical evidence that the new BGMD model does not overfit the data, we compute predictive probabilities for the BGMD model and compare them with those reported for the BGM model [4].

Bottom Line: The former aim to relax the homogeneity assumption, whereas the latter are more flexible and, in principle, more adequate for modelling nonlinear processes.In our paper, we compare both paradigms and discuss theoretical shortcomings of the latter approach.We show that a model based on the changepoint process yields systematically better results than the free allocation model when inferring nonstationary gene regulatory processes from simulated gene expression time series.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, TU Dortmund University, 44221 Dortmund, Germany.

ABSTRACT
An important objective in systems biology is to infer gene regulatory networks from postgenomic data, and dynamic Bayesian networks have been widely applied as a popular tool to this end. The standard approach for nondiscretised data is restricted to a linear model and a homogeneous Markov chain. Recently, various generalisations based on changepoint processes and free allocation mixture models have been proposed. The former aim to relax the homogeneity assumption, whereas the latter are more flexible and, in principle, more adequate for modelling nonlinear processes. In our paper, we compare both paradigms and discuss theoretical shortcomings of the latter approach. We show that a model based on the changepoint process yields systematically better results than the free allocation model when inferring nonstationary gene regulatory processes from simulated gene expression time series. We further cross-compare the performance of both models on three biological systems: macrophages challenged with viral infection, circadian regulation in Arabidopsis thaliana, and morphogenesis in Drosophila melanogaster.

No MeSH data available.


Related in: MedlinePlus