858 Review. Gene network inference C. A. Penfold and D. L. Wild metabolite space number of independent measurements, even for highly resolved and replicated time course studies [6]. The metabolite 1 metabolite 2 sheer number of genes, combined with the observation that a signiﬁcant proportion of expression proﬁles can be correlated over time [6], means that inferring GRNs from microarray data alone may be inherently protein space unidentiﬁable. To overcome this problem, the number protein 2 complex 3–4 protein 4 of genes to be modelled is often artiﬁcially reduced by protein 3 removing ﬂat or uninteresting proﬁles [6] or by cluster- protein 1 ingtogethergroupsofgenesthatmightbeco-expressed [17,18].Alternatively,wheninvestigatinganorganism’s gene space response to a particular stimulus, in which time series gene 2 gene 4 are measured under both control and perturbed con- ditions, the number of genes can be reduced by gene 1 gene 3 including only those that are differentially expressed, i.e.whoseexpressionproﬁlesaredifferentinthecontrol Figure1.AschematicofaGRNadaptedfromBrazhniketal.[1]. and perturbed datasets [19]. Removing genes in this TheGRNconsistsoffourgenes,threeofwhichencodeforTFs waycangreatlylimitthenumbertobemodelled,yield- (genes1,3and4)andoneofwhichencodesforaproteinthat ing ﬁgures in the range of hundreds to tens of catalyses the production of metabolite 2 from metabolite 1.
858 Review. Gene network inference C. A. Penfold and D. L. Wild metabolite space number of independent measurements, even for highly resolved and replicated time course studies [6]. The metabolite 1 metabolite 2 sheer number of genes, combined with the observation that a signiﬁcant proportion of expression proﬁles can be correlated over time [6], means that inferring GRNs from microarray data alone may be inherently protein space unidentiﬁable. To overcome this problem, the number protein 2 complex 3–4 protein 4 of genes to be modelled is often artiﬁcially reduced by protein 3 removing ﬂat or uninteresting proﬁles [6] or by cluster- protein 1 ingtogethergroupsofgenesthatmightbeco-expressed [17,18].Alternatively,wheninvestigatinganorganism’s gene space response to a particular stimulus, in which time series gene 2 gene 4 are measured under both control and perturbed con- ditions, the number of genes can be reduced by gene 1 gene 3 including only those that are differentially expressed, i.e.whoseexpressionproﬁlesaredifferentinthecontrol Figure1.AschematicofaGRNadaptedfromBrazhniketal.[1]. and perturbed datasets [19]. Removing genes in this TheGRNconsistsoffourgenes,threeofwhichencodeforTFs waycangreatlylimitthenumbertobemodelled,yield- (genes1,3and4)andoneofwhichencodesforaproteinthat ing ﬁgures in the range of hundreds to tens of catalyses the production of metabolite 2 from metabolite 1.
Review. Gene network inference C. A. Penfold and D. L. Wild 859 (a) (b) (c) protein space protein 2 X X X X protein 1 protein 3 1 1 2 3 X X X 2 3 1 gene space X X 2 3 gene 2 X X X 3 1 2 gene 1 gene 3 (e) (d) A X1 X1 X1 X1 unobserved X1 X1 X1 C B X X X X 2 2 2 2 X2 X2 X2 X3 X3 X3 X3 observed X X X 3 3 3 D T = 1 T = 2 T = 3 T = N T = 1 T = 2 T = N Figure2.(a)AnexamplesystemcomposedofthreegenesthateachencodeforaTFthatregulatestwoothergenes.TheGRNto be recovered from time-series data is projected into the gene space as dashed lines. The time-series observations represent the mRNAlevelsofgenes1,2and3asX ,X andX ,respectively.(b)AgraphicalrepresentationoftheGRNwewishtorecover.
860 Review. Gene network inference C. A. Penfold and D. L. Wild individualgeneisnolongerrepresentedbyasinglenode priorinformationaboutknownconnectionsinaGRNis ðG Þ but by a series of nodes by unfolding the DAG over encoded using the term p .
860 Review. Gene network inference C. A. Penfold and D. L. Wild individualgeneisnolongerrepresentedbyasinglenode priorinformationaboutknownconnectionsinaGRNis ðG Þ but by a series of nodes by unfolding the DAG over encoded using the term p .
860 Review. Gene network inference C. A. Penfold and D. L. Wild individualgeneisnolongerrepresentedbyasinglenode priorinformationaboutknownconnectionsinaGRNis ðG Þ but by a series of nodes by unfolding the DAG over encoded using the term p .
Review. Gene network inference C. A. Penfold and D. L. Wild 861 2.3.1.Derivativeestimationforcontinuoustimesystems. Beal et al. [7]. An example of inference using non- Microarray time course datasets measure the mRNA parametric NDS can be found in the Matlab package expression proﬁles, X, and consequently, the time- GP4GRN[15].Additionally,weimplementaMatlabver- i derivativeX_ must ﬁrst be estimated from the data in sion of the algorithms proposed in Klemm [35], which i order to apply the continuous non-parametric models includes an EM implementation of a Gaussian process outlined in §2.3. Studies by A¨ıjo¨ & La¨hdesma¨ki [15] model for NDS evolving over continuous time (causal suggest using a discrete approximation: structure identiﬁcation (CSI)c, §2.3), and one evolving ð Þ ð Þ overdiscretetime(CSId,§2.3.2).
Review. Gene network inference C. A. Penfold and D. L. Wild 861 2.3.1.Derivativeestimationforcontinuoustimesystems. Beal et al. [7]. An example of inference using non- Microarray time course datasets measure the mRNA parametric NDS can be found in the Matlab package expression proﬁles, X, and consequently, the time- GP4GRN[15].Additionally,weimplementaMatlabver- i derivativeX_ must ﬁrst be estimated from the data in sion of the algorithms proposed in Klemm [35], which i order to apply the continuous non-parametric models includes an EM implementation of a Gaussian process outlined in §2.3. Studies by A¨ıjo¨ & La¨hdesma¨ki [15] model for NDS evolving over continuous time (causal suggest using a discrete approximation: structure identiﬁcation (CSI)c, §2.3), and one evolving ð Þ ð Þ overdiscretetime(CSId,§2.3.2).
Review. Gene network inference C. A. Penfold and D. L. Wild 861 2.3.1.Derivativeestimationforcontinuoustimesystems. Beal et al. [7]. An example of inference using non- Microarray time course datasets measure the mRNA parametric NDS can be found in the Matlab package expression proﬁles, X, and consequently, the time- GP4GRN[15].Additionally,weimplementaMatlabver- i derivativeX_ must ﬁrst be estimated from the data in sion of the algorithms proposed in Klemm [35], which i order to apply the continuous non-parametric models includes an EM implementation of a Gaussian process outlined in §2.3. Studies by A¨ıjo¨ & La¨hdesma¨ki [15] model for NDS evolving over continuous time (causal suggest using a discrete approximation: structure identiﬁcation (CSI)c, §2.3), and one evolving ð Þ ð Þ overdiscretetime(CSId,§2.3.2).
Review. Gene network inference C. A. Penfold and D. L. Wild 861 2.3.1.Derivativeestimationforcontinuoustimesystems. Beal et al. [7]. An example of inference using non- Microarray time course datasets measure the mRNA parametric NDS can be found in the Matlab package expression proﬁles, X, and consequently, the time- GP4GRN[15].Additionally,weimplementaMatlabver- i derivativeX_ must ﬁrst be estimated from the data in sion of the algorithms proposed in Klemm [35], which i order to apply the continuous non-parametric models includes an EM implementation of a Gaussian process outlined in §2.3. Studies by A¨ıjo¨ & La¨hdesma¨ki [15] model for NDS evolving over continuous time (causal suggest using a discrete approximation: structure identiﬁcation (CSI)c, §2.3), and one evolving ð Þ ð Þ overdiscretetime(CSId,§2.3.2).