Limits...
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

Prior connectivity structure for time series of length m = 26. Graphical heat map representations of the temporal connectivity structures imposed by the prior distribution P(K) · P(V / K) for m = 26 time points. (a) Free allocation model (BGM). (b) Changepoint process (BGMD). Each heat map indicates the prior probability of two time points being assigned to the same compartment. The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0.5. The connectivity strengths were estimated from 10 independent MCMC simulations. In these simulations, an empty data set (without any data points) was used so that the inference was driven exclusively by the prior probability distribution P(K) · P(V / K).
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2913537&req=5

fig9: Prior connectivity structure for time series of length m = 26. Graphical heat map representations of the temporal connectivity structures imposed by the prior distribution P(K) · P(V / K) for m = 26 time points. (a) Free allocation model (BGM). (b) Changepoint process (BGMD). Each heat map indicates the prior probability of two time points being assigned to the same compartment. The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0.5. The connectivity strengths were estimated from 10 independent MCMC simulations. In these simulations, an empty data set (without any data points) was used so that the inference was driven exclusively by the prior probability distribution P(K) · P(V / K).

Mentions: After running 10 independent MCMC simulations with m = 26 to infer the prior distribution P(K) · P(V / K), we can compute the average prior connectivity strengths from the sampled allocation vectors. As before, the fraction of sampled allocation vectors for which two time points ti and tj are allocated to the same componentk (1 ≤ k ≤ K) can be used as a connectivity measure C(ti, tj). Figure 9 shows heat maps of the inferred prior connectivity structure for the free allocation BGM model and the proposed changepoint process BGMD model. The heat maps confirm our earlier conjecture that the proposed BGMD model, which takes the time structure of the data into account, allocates neighbouring time points to the same compartment more likely a priori than the BGM model. More precisely, it can be seen from Figure 9(a) that the prior connectivity strength C(ti, tj) is the same for all ti and tj with ti ≠ tj in the BGM model. On the contrary, for the BGMD model (Figure 9(b)), the connectivity strength C(ti, tj) decreases with the temporal distance between ti and tj: for three time points ti, tj and tk with ti < tj < tk we have C(ti, tj) < C(ti, tk). This finding explains why the proposed BGMD model yields a stronger separation between the light : darkness induced stages in Arabidopsis thaliana (see Figure 4): the two-stage structure of gene-regulation in Arabidopsis is of a temporal form that is supported by the allocation vector prior P(V / K) of the BGMD model.


Modelling nonstationary gene regulatory processes.

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

Prior connectivity structure for time series of length m = 26. Graphical heat map representations of the temporal connectivity structures imposed by the prior distribution P(K) · P(V / K) for m = 26 time points. (a) Free allocation model (BGM). (b) Changepoint process (BGMD). Each heat map indicates the prior probability of two time points being assigned to the same compartment. The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0.5. The connectivity strengths were estimated from 10 independent MCMC simulations. In these simulations, an empty data set (without any data points) was used so that the inference was driven exclusively by the prior probability distribution P(K) · P(V / K).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig9: Prior connectivity structure for time series of length m = 26. Graphical heat map representations of the temporal connectivity structures imposed by the prior distribution P(K) · P(V / K) for m = 26 time points. (a) Free allocation model (BGM). (b) Changepoint process (BGMD). Each heat map indicates the prior probability of two time points being assigned to the same compartment. The probabilities are represented by a grey shading, where white corresponds to a probability of 1, and black corresponds to a probability of 0.5. The connectivity strengths were estimated from 10 independent MCMC simulations. In these simulations, an empty data set (without any data points) was used so that the inference was driven exclusively by the prior probability distribution P(K) · P(V / K).
Mentions: After running 10 independent MCMC simulations with m = 26 to infer the prior distribution P(K) · P(V / K), we can compute the average prior connectivity strengths from the sampled allocation vectors. As before, the fraction of sampled allocation vectors for which two time points ti and tj are allocated to the same componentk (1 ≤ k ≤ K) can be used as a connectivity measure C(ti, tj). Figure 9 shows heat maps of the inferred prior connectivity structure for the free allocation BGM model and the proposed changepoint process BGMD model. The heat maps confirm our earlier conjecture that the proposed BGMD model, which takes the time structure of the data into account, allocates neighbouring time points to the same compartment more likely a priori than the BGM model. More precisely, it can be seen from Figure 9(a) that the prior connectivity strength C(ti, tj) is the same for all ti and tj with ti ≠ tj in the BGM model. On the contrary, for the BGMD model (Figure 9(b)), the connectivity strength C(ti, tj) decreases with the temporal distance between ti and tj: for three time points ti, tj and tk with ti < tj < tk we have C(ti, tj) < C(ti, tk). This finding explains why the proposed BGMD model yields a stronger separation between the light : darkness induced stages in Arabidopsis thaliana (see Figure 4): the two-stage structure of gene-regulation in Arabidopsis is of a temporal form that is supported by the allocation vector prior P(V / K) of the BGMD model.

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