Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Gómez-Gardeñes, Y. Moreno, L. Floría (2005)
On the robustness of complex heterogeneous gene expression networks.Biophysical chemistry, 115 2-3
H. El-Samad, S. Prajna, A. Papachristodoulou, J. Doyle, M. Khammash (2006)
Advanced Methods and Algorithms for Biological Networks AnalysisProceedings of the IEEE, 94
J. Hofbauer (1990)
An index theorem for dissipative semiflowsRocky Mountain Journal of Mathematics, 20
M. Feinberg (1987)
Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theoremsChemical Engineering Science, 42
H. Jong (2002)
Modeling and Simulation of Genetic Regulatory Systems: A Literature ReviewJ. Comput. Biol., 9
YK Kwon (2008)
10.1093/bioinformatics/btn060Bioinformatics, 24
BIOINFORMATICS ORIGINAL PAPER doi:10.1093/bioinformatics/btn060 Systems biology
G. Shinar, R. Milo, María Martínez, U. Alon (2007)
Input–output robustness in simple bacterial signaling systemsProceedings of the National Academy of Sciences, 104
Tianhai Tian (2004)
Robustness of mathematical models for biological systemsAnziam Journal, 45
Hal Smith (1995)
Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith
F. Blanchini, Elisa Franco (2011)
Structurally robust biological networksBMC Systems Biology, 5
Elisa Franco, F. Blanchini (2012)
Structural properties of the MAPK pathway topologies in PC12 cellsJournal of Mathematical Biology, 67
JMG Vilar (2003)
10.1083/jcb.200301125J Cell Biol, 161
H. Sira-Ramírez, R. Castro-Linares (2010)
Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation49th IEEE Conference on Decision and Control (CDC)
Tm Yi, Yun Huang, M. Simon (2000)
Robust perfect adaptation in bacterial chemotaxis through integral feedback control.Proceedings of the National Academy of Sciences of the United States of America, 97 9
Alexander Gorban, O. Radulescu (2007)
Dynamical robustness of biological networks with hierarchical distribution of time scales.IET systems biology, 1 4
H. Kitano (2002)
Systems Biology: A Brief OverviewScience, 295
G. Shinar, M. Feinberg (2010)
Structural Sources of Robustness in Biochemical Reaction NetworksScience, 327
Eduardo Sontag (2007)
Monotone and near-monotone biochemical networksSystems and Synthetic Biology, 1
(2008)
Set-theoretic methods in control, Vol 22 of Systems and Control: Foundations and Applications
T. Drengstig, H. Ueda, P. Ruoff (2008)
Predicting perfect adaptation motifs in reaction kinetic networks.The journal of physical chemistry. B, 112 51
F. Blanchini, S. Miani (2007)
Set-theoretic methods in control
Wenzhe Ma, A. Trusina, H. El-Samad, W. Lim, Chao Tang (2009)
Defining Network Topologies that Can Achieve Biochemical AdaptationCell, 138
Frederick Balagaddé, Hao Song, Junichi Ozaki, C. Collins, Mat Barnet, F. Arnold, S. Quake, L. You (2008)
A synthetic Escherichia coli predator–prey ecosystemMolecular Systems Biology, 4
Ö. Kartal, O. Ebenhöh (2009)
Ground State Robustness as an Evolutionary Design Principle in Signaling NetworksPLoS ONE, 4
A. Ambrosetti, G. Prodi (1993)
A primer of nonlinear analysis
A. Abate, A. Tiwari, S. Sastry (2007)
Box invariance for biologically-inspired dynamical systems2007 46th IEEE Conference on Decision and Control
R. Prill, P. Iglesias, A. Levchenko (2005)
Dynamic Properties of Network Motifs Contribute to Biological Network OrganizationPLoS Biology, 3
S. Nikolov, E. Yankulova, O. Wolkenhauer, V. Petrov (2007)
Principal difference between stability and structural stability (robustness) as used in systems biology.Nonlinear dynamics, psychology, and life sciences, 11 4
J. Meiss (2007)
Differential dynamical systems, 14
D. Angeli, J. Ferrell, Eduardo Sontag (2004)
Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systemsProceedings of the National Academy of Sciences of the United States of America, 101
(2004)
Robustness ofmathematicalmodels for biological systems
J. Vilar, C. Guet, S. Leibler (2004)
Modeling network dynamics: the lac operon, a case studyarXiv: Molecular Networks
M. Aldana, P. Cluzel (2003)
A natural class of robust networksProceedings of the National Academy of Sciences of the United States of America, 100
Silvia Santos, P. Verveer, P. Bastiaens (2007)
Growth factor-induced MAPK network topology shapes Erk response determining PC-12 cell fateNature Cell Biology, 9
J. Ackermann, B. Wlotzka, J. McCaskill (1998)
In vitro DNA-based predator-prey system with oscillatory kineticsBulletin of Mathematical Biology, 60
J. Jacquez, C. Simon (1993)
Qualitative Theory of Compartmental SystemsSIAM Rev., 35
R. Ortega (1995)
Some applications of the topological degree to stability theory
A. Goldbeter, Claude Gérard, D. Gonze, J. Leloup, Geneviève Dupont (2012)
Systems biology of cellular rhythmsFEBS Letters, 586
[We introduce the idea of structural analysis of biological network models. In general, mathematical representations of molecular systems are affected by parametric uncertainty: experimental validation of models is always affected by errors and intrinsic variability of biological samples. Using uncertain models for predictions is a delicate task. However, given a plausible representation of a system, it is often possible to reach general analytical conclusions on the system’s admissible dynamic behaviors, regardless of specific parameter values: in other words, we say that certain behaviors are structural for a given model. Here we describe a parameter-free, qualitative modeling framework and we focus on several case studies, showing how many paradigmatic behaviors such as multistationarity or oscillations can have a structural nature. We highlight that classical control theory methods are extremely helpful in investigating structural properties.]
Published: Jul 4, 2014
Keywords: Biological network; Control theory; Structural analysis; Structural property; Enzymatic networks; Jacobian; Eigenvalue; Chemical reaction network; Robustness; Set invariance; Mitogen activated protein kinase (MAPK)
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.