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==History==

==History==

The study of network motifs was pioneered by Holland and Leinhardt<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> who introduced the concept of a triad census of networks. They introduced methods to enumerate various types of subgraph configurations, and test whether the subgraph counts are statistically different from those expected in random networks.  

The study of network motifs was pioneered by Holland and Leinhardt<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> who introduced the concept of a triad census of networks. They introduced methods to enumerate various types of subgraph configurations, and test whether the subgraph counts are statistically different from those expected in random networks.  

This idea was further generalized in 2002 by [[Uri Alon]] and his group <ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> when network motifs were discovered in the gene regulation (transcription) network of the bacteria ''[[Escherichia coli|E. coli]]'' and then in a large set of natural networks. Since then, a considerable number of studies have been conducted on the subject. Some of these studies focus on the biological applications, while others focus on the computational theory of network motifs.

This idea was further generalized in 2002 by [[Uri Alon]] and his group <ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> when network motifs were discovered in the gene regulation (transcription) network of the bacteria ''[[Escherichia coli|E. coli]]'' and then in a large set of natural networks. Since then, a considerable number of studies have been conducted on the subject. Some of these studies focus on the biological applications, while others focus on the computational theory of network motifs.

The biological studies endeavor to interpret the motifs detected for biological networks. For example, in work following,<ref name="she1" /> the network motifs found in ''[[Escherichia coli|E. coli]]'' were discovered in the transcription networks of other bacteria<ref name="eic1">{{cite journal  |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} {{open access}}</ref> as well as yeast<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal  |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref> and higher organisms.<ref name="odo1">{{cite journal  |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal  |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref> A distinct set of network motifs were identified in other types of biological networks such as neuronal networks and protein interaction networks.<ref name="mil2" /><ref name="maa1">{{cite journal  |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal  |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref>

The biological studies endeavor to interpret the motifs detected for biological networks. For example, in work following,<ref name="she1" /> the network motifs found in ''[[Escherichia coli|E. coli]]'' were discovered in the transcription networks of other bacteria<ref name="eic1">{{cite journal  |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} {{open access}}</ref> as well as yeast<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal  |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref> and higher organisms.<ref name="odo1">{{cite journal  |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal  |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref> A distinct set of network motifs were identified in other types of biological networks such as neuronal networks and protein interaction networks.<ref name="mil2" /><ref name="maa1">{{cite journal  |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal  |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref>

The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section in chronological order.

The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section in chronological order.

Most recently, the acc-MOTIF tool to detect network motifs was released.<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref>

Most recently, the acc-MOTIF tool to detect network motifs was released.<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref>

==Motif discovery algorithms==

==Motif discovery algorithms==