Cellular automata simulation of topological effects on the dynamics of feed-forward motifs

Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Apte, Advait A [verfasserIn] Cain, John W Bonchev, Danail G Fong, Stephen S

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2008

Schlagwörter:	Cellular Automaton Lattice Density Cellular Automaton Model Topological Effect

Anmerkung:	© Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (

Übergeordnetes Werk:	Enthalten in: Journal of biological engineering - Berlin : Springer, 2007, 2(2008), 1 vom: 27. Feb.
Übergeordnetes Werk:	volume:2 ; year:2008 ; number:1 ; day:27 ; month:02

Links:	Volltext

DOI / URN:	10.1186/1754-1611-2-2

Katalog-ID:	SPR029566479

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520			\|a Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models.
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allfields	10.1186/1754-1611-2-2 doi (DE-627)SPR029566479 (SPR)1754-1611-2-2-e DE-627 ger DE-627 rakwb eng Apte, Advait A verfasserin aut Cellular automata simulation of topological effects on the dynamics of feed-forward motifs 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. Cellular Automaton (dpeaa)DE-He213 Cellular Automaton (dpeaa)DE-He213 Lattice Density (dpeaa)DE-He213 Cellular Automaton Model (dpeaa)DE-He213 Topological Effect (dpeaa)DE-He213 Cain, John W aut Bonchev, Danail G aut Fong, Stephen S aut Enthalten in Journal of biological engineering Berlin : Springer, 2007 2(2008), 1 vom: 27. Feb. (DE-627)54689884X (DE-600)2391582-1 1754-1611 nnns volume:2 year:2008 number:1 day:27 month:02 https://dx.doi.org/10.1186/1754-1611-2-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2008 1 27 02
spelling	10.1186/1754-1611-2-2 doi (DE-627)SPR029566479 (SPR)1754-1611-2-2-e DE-627 ger DE-627 rakwb eng Apte, Advait A verfasserin aut Cellular automata simulation of topological effects on the dynamics of feed-forward motifs 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. Cellular Automaton (dpeaa)DE-He213 Cellular Automaton (dpeaa)DE-He213 Lattice Density (dpeaa)DE-He213 Cellular Automaton Model (dpeaa)DE-He213 Topological Effect (dpeaa)DE-He213 Cain, John W aut Bonchev, Danail G aut Fong, Stephen S aut Enthalten in Journal of biological engineering Berlin : Springer, 2007 2(2008), 1 vom: 27. Feb. (DE-627)54689884X (DE-600)2391582-1 1754-1611 nnns volume:2 year:2008 number:1 day:27 month:02 https://dx.doi.org/10.1186/1754-1611-2-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2008 1 27 02
allfields_unstemmed	10.1186/1754-1611-2-2 doi (DE-627)SPR029566479 (SPR)1754-1611-2-2-e DE-627 ger DE-627 rakwb eng Apte, Advait A verfasserin aut Cellular automata simulation of topological effects on the dynamics of feed-forward motifs 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. Cellular Automaton (dpeaa)DE-He213 Cellular Automaton (dpeaa)DE-He213 Lattice Density (dpeaa)DE-He213 Cellular Automaton Model (dpeaa)DE-He213 Topological Effect (dpeaa)DE-He213 Cain, John W aut Bonchev, Danail G aut Fong, Stephen S aut Enthalten in Journal of biological engineering Berlin : Springer, 2007 2(2008), 1 vom: 27. Feb. (DE-627)54689884X (DE-600)2391582-1 1754-1611 nnns volume:2 year:2008 number:1 day:27 month:02 https://dx.doi.org/10.1186/1754-1611-2-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2008 1 27 02
allfieldsGer	10.1186/1754-1611-2-2 doi (DE-627)SPR029566479 (SPR)1754-1611-2-2-e DE-627 ger DE-627 rakwb eng Apte, Advait A verfasserin aut Cellular automata simulation of topological effects on the dynamics of feed-forward motifs 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. Cellular Automaton (dpeaa)DE-He213 Cellular Automaton (dpeaa)DE-He213 Lattice Density (dpeaa)DE-He213 Cellular Automaton Model (dpeaa)DE-He213 Topological Effect (dpeaa)DE-He213 Cain, John W aut Bonchev, Danail G aut Fong, Stephen S aut Enthalten in Journal of biological engineering Berlin : Springer, 2007 2(2008), 1 vom: 27. Feb. (DE-627)54689884X (DE-600)2391582-1 1754-1611 nnns volume:2 year:2008 number:1 day:27 month:02 https://dx.doi.org/10.1186/1754-1611-2-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2008 1 27 02
allfieldsSound	10.1186/1754-1611-2-2 doi (DE-627)SPR029566479 (SPR)1754-1611-2-2-e DE-627 ger DE-627 rakwb eng Apte, Advait A verfasserin aut Cellular automata simulation of topological effects on the dynamics of feed-forward motifs 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. Cellular Automaton (dpeaa)DE-He213 Cellular Automaton (dpeaa)DE-He213 Lattice Density (dpeaa)DE-He213 Cellular Automaton Model (dpeaa)DE-He213 Topological Effect (dpeaa)DE-He213 Cain, John W aut Bonchev, Danail G aut Fong, Stephen S aut Enthalten in Journal of biological engineering Berlin : Springer, 2007 2(2008), 1 vom: 27. Feb. (DE-627)54689884X (DE-600)2391582-1 1754-1611 nnns volume:2 year:2008 number:1 day:27 month:02 https://dx.doi.org/10.1186/1754-1611-2-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2008 1 27 02
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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. 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author	Apte, Advait A
spellingShingle	Apte, Advait A misc Cellular Automaton misc Lattice Density misc Cellular Automaton Model misc Topological Effect Cellular automata simulation of topological effects on the dynamics of feed-forward motifs
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topic_title	Cellular automata simulation of topological effects on the dynamics of feed-forward motifs Cellular Automaton (dpeaa)DE-He213 Lattice Density (dpeaa)DE-He213 Cellular Automaton Model (dpeaa)DE-He213 Topological Effect (dpeaa)DE-He213
topic	misc Cellular Automaton misc Lattice Density misc Cellular Automaton Model misc Topological Effect
topic_unstemmed	misc Cellular Automaton misc Lattice Density misc Cellular Automaton Model misc Topological Effect
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title	Cellular automata simulation of topological effects on the dynamics of feed-forward motifs
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title_full	Cellular automata simulation of topological effects on the dynamics of feed-forward motifs
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title_sort	cellular automata simulation of topological effects on the dynamics of feed-forward motifs
title_auth	Cellular automata simulation of topological effects on the dynamics of feed-forward motifs
abstract	Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (
abstractGer	Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (
abstract_unstemmed	Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems. Results Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production. Conclusion It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models. © Apte et al; licensee BioMed Central Ltd. 2008. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (
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title_short	Cellular automata simulation of topological effects on the dynamics of feed-forward motifs
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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Background Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. 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Cellular automata simulation of topological effects on the dynamics of feed-forward motifs

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