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Simplicity within Complexity: Understanding dynamics of cellular networks by model reduction
Stockholm University, Faculty of Science, Department of Biochemistry and Biophysics.
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Cellular networks composed of interactions between genes, proteins and metabolites, determines the behavioural repertoire of the cell. Recent developments in high-throughput experimental techniques and computational methods allow static descriptions of these networks on a genome scale. There are also several dynamical mathematical models characterizing small subnetworks of the cell such as a signaling cascade or cell division. These networks exhibit a considerable complexity, and mathematical analysis are therefore essential in order to uncover the underlying dynamical core driving the systems. A core description can reveal the relative functional contributions of the various molecular interactions and goes to the heart of what kind of computations biological circuits perform. Partially successful methodologies toward this end includes bifurcation analysis, which only considers a small number of dimensions, and large-scale computer simulations.

In this thesis we explore a third route utilizing the inherent biological structure and dynamics of the network as a tool for model simplification. Using the well studied cell cycle, as a model system, we observe that the this network can be divided into dynamical modules displaying a switch-like behaviour. This allows a transformation into a piecewise linear system with delay, the subsequent use of tools from linear systems theory and finally a core dynamical description. Analytical expressions capturing important cell cycle features such as cell mass, as well as necessary constraints for cell cycle oscillations, are thereby retrieved. Finally we use the dynamical core together with large-scale simulations in order to study the balance between robustness and sensitivity.

It appears that biological features such as switches, modularity and robustness provide a means to reformulate intractable mathematical problems into solvable ones, as biology appears to suggest a path of simplicity within the realm of mathematical complexity.

Place, publisher, year, edition, pages
Stockholm: Institutionen för biokemi och biofysik , 2008. , 200 p.
Keyword [en]
model reduction, cellular networks, dynamical modules, delayed piecewise linear, systems biology
National Category
Biochemistry and Molecular Biology
Research subject
Biochemistry
Identifiers
URN: urn:nbn:se:su:diva-8333ISBN: 978-91-7155-789-6 (print)OAI: oai:DiVA.org:su-8333DiVA: diva2:200100
Public defence
2008-12-12, Magnélisalen, Kemiska övningslaboratoriet, Svante Arrhenius väg 12 A, Stockholm, 13:00
Opponent
Supervisors
Available from: 2008-11-20 Created: 2008-11-19 Last updated: 2011-01-13Bibliographically approved
List of papers
1. Modeling complex cellular networks: Robust switching in the cell cycle ensures a piecewise linear reduction of the regulatory network
Open this publication in new window or tab >>Modeling complex cellular networks: Robust switching in the cell cycle ensures a piecewise linear reduction of the regulatory network
2004 In: CDC 2004: IEEE Conference on Decision and Control, ISSN 0191-2216, Vol. 1, 117-123 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:su:diva-25629 (URN)
Note
Part of urn:nbn:se:su:diva-8333Available from: 2008-11-20 Created: 2008-11-19Bibliographically approved
2. Deconstructing the core dynamics from a complex time-lagged regulatory biological circuit
Open this publication in new window or tab >>Deconstructing the core dynamics from a complex time-lagged regulatory biological circuit
Show others...
2009 (English)In: IET systems biology, ISSN 1751-8849, Vol. 3, no 2, 113-129 p.Article in journal (Refereed) Published
Abstract [en]

Complex regulatory dynamics is ubiquitous in molecular networks composed of genes and proteins. Recent progress in computational biology and its application to molecular data generate a growing number of complex networks. Yet, it has been difficult to understand the governing principles of these networks beyond graphical analysis or extensive numerical simulations. Here the authors exploit several simplifying biological circumstances which thereby enable to directly detect the underlying dynamical regularities driving periodic oscillations in a dynamical nonlinear computational model of a protein-protein network. System analysis is performed using the cell cycle, a mathematically well-described complex regulatory circuit driven by external signals. By introducing an explicit time delay and using a -tearing-and-zooming- approach the authors reduce the system to a piecewise linear system with two variables that capture the dynamics of this complex network. A key step in the analysis is the identification of functional subsystems by identifying the relations between state-variables within the model. These functional subsystems are referred to as dynamical modules operating as sensitive switches in the original complex model. By using reduced mathematical representations of the subsystems the authors derive explicit conditions on how the cell cycle dynamics depends on system parameters, and can, for the first time, analyse and prove global conditions for system stability. The approach which includes utilising biological simplifying conditions, identification of dynamical modules and mathematical reduction of the model complexity may be applicable to other well-characterised biological regulatory circuits.

Keyword
biochemistry, biology computing, cellular biophysics, genetics, molecular biophysics, proteins
National Category
Medical Biotechnology (with a focus on Cell Biology (including Stem Cell Biology), Molecular Biology, Microbiology, Biochemistry or Biopharmacy)
Identifiers
urn:nbn:se:su:diva-25630 (URN)10.1049/iet-syb.2007.0028 (DOI)000264454600005 ()
Available from: 2008-11-20 Created: 2008-11-19 Last updated: 2011-02-16Bibliographically approved
3. Decoding complex biological networks: Sensitive parameter combinations identified by a reduced model
Open this publication in new window or tab >>Decoding complex biological networks: Sensitive parameter combinations identified by a reduced model
Manuscript (Other academic)
Identifiers
urn:nbn:se:su:diva-25631 (URN)
Note
Part of urn:nbn:se:su:diva-8333Available from: 2008-11-20 Created: 2008-11-19 Last updated: 2010-01-13Bibliographically approved
4. On Stability of Limit Cycles of a Prototype Problem of Piecewise Linear Systems
Open this publication in new window or tab >>On Stability of Limit Cycles of a Prototype Problem of Piecewise Linear Systems
2010 (English)In: Emergent Problems in Nonlinear Systems and Control / [ed] Bijoy K. Ghosh, Clyde F. Martin, Yishao Zhou, Berlin: Springer , 2010, 43-55 p.Chapter in book (Other academic)
Place, publisher, year, edition, pages
Berlin: Springer, 2010
Series
Lecture Notes in Control and Information Sciences, ISSN 0170-8643 ; 393
Identifiers
urn:nbn:se:su:diva-33952 (URN)978-3-642-03626-2 (ISBN)
Available from: 2009-12-31 Created: 2009-12-31 Last updated: 2011-01-13Bibliographically approved

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