title: Effects of small particle numbers on long-term behaviour in discrete biochemical systems.
abstract: BACKGROUND
  The functioning of many biological processes depends on the appearance of only a small number of a single molecular species. Additionally, the observation of molecular crowding leads to the insight that even a high number of copies of species do not guarantee their interaction. How single particles contribute to stabilizing biological systems is not well understood yet. Hence, we aim at determining the influence of single molecules on the long-term behaviour of biological systems, i.e. whether they can reach a steady state.
  
  
  RESULTS
  We provide theoretical considerations and a tool to analyse Systems Biology Markup Language models for the possibility to stabilize because of the described effects. The theory is an extension of chemical organization theory, which we called discrete chemical organization theory. Furthermore we scanned the BioModels Database for the occurrence of discrete chemical organizations. To exemplify our method, we describe an application to the Template model of the mitotic spindle assembly checkpoint mechanism.
  
  
  METHODS
  http://www.biosys.uni-jena.de/Services.html.
  
  
  BACKGROUND
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia.
authors.forename: Peter
authors.initials: P
authors.lastname: Kreyssig
authors.affiliation: Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia.
authors.forename: Christian
authors.initials: C
authors.lastname: Wozar
authors.affiliation: Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia.
authors.forename: Stephan
authors.initials: S
authors.lastname: Peter
authors.affiliation: Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia.
authors.forename: Tomás
authors.initials: T
authors.lastname: Veloz
authors.affiliation: Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia.
authors.forename: Bashar
authors.initials: B
authors.lastname: Ibrahim
authors.affiliation: Bio Systems Analysis Group, Department of Mathematics and Computer Science and Jena Centre for Bioinformatics, Friedrich Schiller University Jena, 07743 Jena, Germany, Mathematics Department, University of British Columbia, Kelowna, BC V1V 1V7, Canada, Instituto de Filosofía y Ciencias de la Complejidad - IFICC, Los Alerces 3024 Ñuñoa, Santiago, Chile, Center Leo Apostel, Vrije Universiteit Brussel, B-1160 Brussels, Belgium, Umm Al-Qura University, 1109 Makkah Al-Mukarramah and Al-Qunfudah Center for Scientific Research (QCSR), 21912 Al-Qunfudah, Kingdom of Saudi Arabia.
authors.forename: Peter
authors.initials: P
authors.lastname: Dittrich
mesh_terms: D016208:Databases, Factual; D008954:Models, Biological; D008941:Spindle Apparatus / Q000502:physiology; D049490:Systems Biology / Q000379:methods