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Systems Biology. Today’s lecture will cover the following three topics. Introduction to transcriptional networks Regulation of the expression of the Lac operon Finding Biclusters in Bipartite Graphs. transcriptional networks.

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Introduction to transcriptional networks Regulation of the expression of the Lac operon

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Introduction to transcriptional networks regulation of the expression of the lac operon

Systems Biology

Today’s lecture will cover the following three topics

  • Introduction to transcriptional networks

  • Regulation of the expression of the Lac operon

  • Finding Biclusters in Bipartite Graphs


Introduction to transcriptional networks regulation of the expression of the lac operon

transcriptional networks

By the term transcriptional networks we generally mean gene regulatory networks

Unlike protein-protein interaction networks the transcriptional networks are directed networks


Introduction to transcriptional networks regulation of the expression of the lac operon

transcriptional networks: Basic mechanism of gene regulation


Introduction to transcriptional networks regulation of the expression of the lac operon

transcriptional networks


Introduction to transcriptional networks regulation of the expression of the lac operon

transcriptional networks

Most genes are regulated at transcription level and it is assumed that 5-10% of protein coding genes encode regulatory proteins.

Some regulatory proteins play targeted role i.e. they take part in regulation of a few genes.

Some regulatory proteins play more general role in initiating transcription (for example the eukaryotic transcription factors of type II or the RNA polymerase itself that is essential for the transcription of all genes).

It is considered that dedicated regulatory proteins are those that affect up to 5% genes of a genome.

However the boundary between the generalist and dedicated regulatory proteins is blurred.


Introduction to transcriptional networks regulation of the expression of the lac operon

transcriptional networks

  • Experiments and methods used to determine regulatory relations

  • Complementary DNA microarrays

  • Oligonucleotide chips

  • Reverse transcription polymerase chain reaction

  • Serial analysis of gene expression

  • Chromatin Immunoprecipitation

  • Bioinformatics—e.g. by way of identifying binding sites


Introduction to transcriptional networks regulation of the expression of the lac operon

  • Transcriptional Networks: Case study 1

  • An extended transcriptional regulatory network of Escherichia coli and analysis of its hierarchical structure and network motifs

  • Hong-Wu Ma, Bharani Kumar, Uta Ditges2, Florian Gunzer2, Jan Buer1,2 and An-Ping Zeng*

  • Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

  • This work combined data sets from 3 different sources:

  • RegulonDB (version 4.0, http://www.cifn.unam.mx/Computational_Genomics/regulondb/)

  • Ecocyc (version 8.0, www.ecocyc.org)

  • Shen-Orr,S.S., Milo,R., Mangan,S. and Alon,U. (2002) Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genet., 31, 64–68.


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

Comparison of the TRN of E.coli from three different data sources (A) Based on number of genes (B) Based on number regulatory interactions


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

A combined network that includes all the 2624 interactions from the three data sets has been produced.

In addition, this work extended this network by adding 23 additional genes and around 100 regulatory relationships through literature survey.

The final TRN altogether includes 1278 genes and 2724 interactions.


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

  • This work discovered a hierarchical structure in the TRN.

  • The hierachical structure was identified according to the following way:

  • genes which do not code for transcription factors (TFs) or code for a TF which only regulates its own expression (auto-regulatory loop) were assigned to layer 1 (the lowest layer);

  • then we removed all the genes in layer 1 and from the remaining network identified TFs which do not regulate other genes and assigned the corresponding genes in layer 2;

  • we repeated step 2 to remove nodes which have been assigned to a layer and identified a new layer until all the genes were assigned to different layers. As a result, a nine layer hierarchical structure was uncovered.

From BMC Bioinformatics 2004, 5:199 of the related authors


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

The hierarchical structure implies absence of cycles in the network i.e. feedback loops (though auto regulatory and inter-regulatory loops exist)

As the network is not complete, we cannot say that feedback loop could not be found in future however it seems they would not be too many.

A possible biological explanation for the existence of this hierarchical structure is that the interactions in this particular TRN are between proteins and genes without involving metabolites.

Only after a regulating gene has been transcribed, translated and eventually further modified by cofactors or other proteins, it can

regulate the target gene.

A feedback from the regulated gene at transcriptional level may delay the process for the target gene to access a desired expression level in a new environment.


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

Feedback control may be mainly through other interactions (e.g. metabolite and protein interaction) at post-transcriptional level rather than through transcriptional interactions between proteins and genes.

For example, a gene at the bottom layer may code for a metabolic enzyme, the product of which can bind to a regulator which in turn regulates its expression. In this case, the feedback is through metabolite–protein interaction to change the activity of the transcription factor and then to affect the expression of the regulated gene.

Therefore, to fully understand the gene expression regulation, an integrated network that includes different interactions is needed.


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

To calculate network motifs in the E.coli TRN, this work removed all the loops in the network (including the autoregulatory loops and the two-gene regulatory loops). Then they used the program Mfinder developed by Kashtan et al. to generate the motif profiles.

The first four types are the so-called coherent FFLs in which the direct effect of the up regulator is consistent with its indirect effect through the mid regulator.

In contrast, the last four types of FFLs are incoherent because the direct effect of the up regulator is contradictive with its indirect effect


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649

(A) Gene gadA is regulated by six FFLs (B)Gene lpd is regulated by five FFLs (C) Gene slp is regulated by 17 regulators


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 1

Nucleic Acids Research, 2004, Vol. 32, No. 22 6643–6649


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 2

Topological and causal structure of the yeast transcriptional regulatory network

Nabil Guelzim1,2, Samuele Bottani3, Paul Bourgine2 & François Képès1

nature genetics • volume 31 • may 2002

In this work the yeast transcriptional network was constructed by manual inspection of the websites of MIPS, SwissProt, Yeast Protein Database, S. cerevisiae Promoter Database and the Saccharomyces Genome Database

The network consists of 491 genes and 909 regulatory relations


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 2

nature genetics • volume 31 • may 2002

The network consists of 491 genes and 909 regulatory relations

Bold type indicates self-activation, bold italics indicates self-inhibition and borders indicate essential genes. Thick lines represent activation, thin lines represent inhibition and the dashed gray line represents dual regulation.


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 2

nature genetics • volume 31 • may 2002

Indegree distribution of this yeast transcriptional network is exponential

Typical exponential distribution on normal scale


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 2

nature genetics • volume 31 • may 2002

Indegree distribution of this yeast transcriptional network is exponential

open squares, full line --for all 402 regulated genes (367 nonregulatory and 35 interregulatory genes), 909 connections, p(k)=157e–0.45k; R=0.99)

filled circles, broken line ---for the subset of 35 interregulatory genes, 72 connections; p(k)=15e–0.43k; R=0.94

Indegree distribution of the transcriptional network on semi-log scale


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 2

nature genetics • volume 31 • may 2002

Outdegree distribution of this yeast transcriptional network follows power law

Typical power law distribution on normal scale


Introduction to transcriptional networks regulation of the expression of the lac operon

Transcriptional Network: Case study 2

nature genetics • volume 31 • may 2002

Outdegree distribution of this yeast transcriptional network follows power law

Open squares, full line --for all 124 regulating proteins (909 connections; P(k)=23k−0.87; R=0.95)

filled circles, broken line – for 37 regulating proteins that control regulatory genes (72 connections; P(k)=19k−1.14; R=0.99)

Outdegree distribution of the transcriptional network on log-log scale


Introduction to transcriptional networks regulation of the expression of the lac operon

The operon

an operon is a functioning unit of genomic material containing a cluster of genes under the control of a single regulatory signal or promoter.

The genes are transcribed together into an mRNA strand and either translated together in the cytoplasm, or undergo trans-splicing to create monocistronic mRNAs that are translated separately.

The result of this is that the genes contained in the operon are either expressed together or not at all.

Originally operons were thought to exist solely in prokaryotes but since the discovery of the first operons in eukaryotes in the early 1990s, more evidence has arisen to suggest they are more common than previously assumed.


Introduction to transcriptional networks regulation of the expression of the lac operon

The Lac operon

The lac operon of e.coli consists of three genes LacZ, LacY and LacA

They are the codes of enzymes needed for processing lactose

LacI is an adjacent gene which is a regulator ( transcriptional repressor) of the Lac operon

Besides the promoter operator region there is a region where a complex called CAP binds which affect the transcription positively

LacZ codes for the enzyme B-galactosidase and LacY codes for lactose permease, an enzyme that facilitates the flux of lactose through the cell membrane

LacA is not directly involved in processing Lactose

Source: Models of cellular regulation by Baltazar D. Aguda and Avner Friedman


Introduction to transcriptional networks regulation of the expression of the lac operon

The Lac operon

The LacI tetramer binds at the promoter region and stops the transcription

The CAP complex binds the cap region and enhance the binding of RNA polymerase

Static model of the regulation of the expression of the Lac operon

Source: Models of cellular regulation by Baltazar D. Aguda and Avner Friedman


Introduction to transcriptional networks regulation of the expression of the lac operon

cAMP binds and LacI is suppressed by Allolactose

cAMP cannot bind and repressor protein LacI binds

cAMP binds and repressor protein LacI binds

cAMP cannot bind and LacI is suppressed by Allolactose

Summary in Table


Introduction to transcriptional networks regulation of the expression of the lac operon

  • Introduction to transcriptional networks

  • Regulation of the expression of the Lac operon

  • Finding Biclusters in Bipartite Graphs

The technique of finding biclusters can be used to determine co-expressed gene groups


Introduction to transcriptional networks regulation of the expression of the lac operon

Definition of a bicluster

Given a nxp data matrix X, where n is the number of objects (e.g. genes) and p is the number of conditions (e.g. array), a bicluster is defined as a submatrix XIJ of X within which a subset of objects I express similar behavior across the subset of conditions J.

A nxp data matrix X can be easily converted to a bipartite graph by considering a threshold or so.

Finding bicluster (densely connected regions) in a bipartite graph is a similar problem.


Introduction to transcriptional networks regulation of the expression of the lac operon

V1

V2

A Graph G=(V,E) is bipartite if its vertex set V can be partitioned into two subsets V1, V2 such that each edge of E has one end vertex in V1 and another in V2.


Introduction to transcriptional networks regulation of the expression of the lac operon

Biclusters are densely connected regions in a bipartite graph


Introduction to transcriptional networks regulation of the expression of the lac operon

Gene expression data can be represented as bipartite graphs

Before transforming, the data can be normalized

Biclusters in gene expression data represents transcription modules/co-expressed gene groups

By transforming highest 5% values to 1


Introduction to transcriptional networks regulation of the expression of the lac operon

  • Tanay,A. et al. (2002) Discovering statistically significant biclusters in gene expression data. Bioinformatics, 18 (Suppl. 1), S136–S144.

  • Ihmels,J. et al. (2002) Revealing modular organization in the yeast transcriptional network. Nat. Genet., 31, 370–377.

  • Ben-Dor,A., Chor,B., Karp,R. and Yakhini,Z. (2002) Discovering local structure in gene expression data: the order-preserving sub-matrix problem. In Proceedings of the 6th Annual International Conference on Computational Biology, ACM Press, New York, NY, USA, pp. 49–57.

  • Cheng,Y. and Church,G. (2000) Biclustering of expression data. Proc. Int. Conf. Intell. Syst. Mol. Biol. pp. 93–103.

  • Murali,T.M. and Kasif,S. (2003) Extracting conserved gene expression motifs from gene expression data. Pac. Symp. Biocomput., 8, 77–88.


We propose a biclustering method incorporating dpclus

We propose a biclustering method incorporating DPClus

An example bipartite graph and its corresponding matrix

(for ik)


Biclus biclustering method incorporating dpclus

BiClus:Biclustering method incorporating DPClus

Concerning each row i (i=0 to |G|-1) of MCN, we calculate thresholdi=avgi+(maxi- avgi)  Gmargin

and set (MSG)ik =(MSG)ki=1if (MCN)ikthresholdi and thresholdi is not an indeterminate number (for k=0 to |G|-1).

Here, avgi = SUMi/niwhere ni is the number of non-zero entries in row i of MCN

and maxiis the maximum value of the entries in row i of MCN

Gmargin is a user defined value 1.

Common neighbor matrix of the bipartite graph


Introduction to transcriptional networks regulation of the expression of the lac operon

BiClus:Biclustering method incorporating DPClus

This matrix represents a simple graph


Introduction to transcriptional networks regulation of the expression of the lac operon

BiClus:Biclustering method incorporating DPClus

Simple graph derived from the common neighbor matrix.

We can use DPClus to find clusters in the simple graph.


Introduction to transcriptional networks regulation of the expression of the lac operon

BiClus:Biclustering method incorporating DPClus

Clustering by DPClus


Introduction to transcriptional networks regulation of the expression of the lac operon

BiClus:Biclustering method incorporating DPClus

Clustering by DPClus


Introduction to transcriptional networks regulation of the expression of the lac operon

Finally determined biclusters

BiClus:Biclustering method incorporating DPClus


Introduction to transcriptional networks regulation of the expression of the lac operon

Evaluation of BiClus

-Using Synthetic data

-Using real data


Introduction to transcriptional networks regulation of the expression of the lac operon

Evaluation of BiClus

Synthetic data

Artificially embedded biclusters with noise


Introduction to transcriptional networks regulation of the expression of the lac operon

Evaluation of BiClus

Synthetic data

Artificially embedded biclusters with overlap


Introduction to transcriptional networks regulation of the expression of the lac operon

Evaluation of BiClus

Let M1, M2 be two sets of biclusters. The gene match score of M1 with respect to M2 is given by the function

A systematic comparison and evaluation of biclustering methods

for gene expression data

Amela Prelic´, Stefan Bleuler, Philip Zimmermann, Anja Wille, Peter Bu¨ hlmann, Wilhelm Gruissem, Lars Hennig, Lothar Thiele and Eckart Zitzle

BIOINFORMATICS, Vol. 22 no. 9 2006, pages 1122–1129


Introduction to transcriptional networks regulation of the expression of the lac operon

Evaluation of BiClus

Synthetic data

Artificially embedded biclusters with noise


Introduction to transcriptional networks regulation of the expression of the lac operon

Evaluation of BiClus

Synthetic data

Artificially embedded biclusters with overlap


Introduction to transcriptional networks regulation of the expression of the lac operon

Gasch,A.P. et al. (2000) Genomic expression programs in the response

of yeast cells to environmental changes. Mol. Biol. Cell, 11, 4241–4257.

Gene expression data collected from the above work


Introduction to transcriptional networks regulation of the expression of the lac operon

Gene expression data can be represented as bipartite graphs

Before transforming, the data can be normalized

Biclusters in gene expression data represents transcription modules

By transforming highest 5% values to 1


Introduction to transcriptional networks regulation of the expression of the lac operon

0.001

0.002

0.003

0.01

Evaluation of BiClus

Real gene expression data of yeast

P-values represents statistical significance of functional richness of the modules

P-Values calculated using FuncAssociate: The Gene Set Functionator from

http://llama.med.harvard.edu/cgi/func/funcassociate


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