| 1. |
- Eriksson, Olivia, 1971-
(author)
-
Simplicity within Complexity : Understanding dynamics of cellular networks by model reduction
- 2008
-
Doctoral thesis (other academic/artistic)abstract
- 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.
|
|
| 2. |
- Bernhardsson, Sebastian, 1980-
(author)
-
Structures in complex systems : Playing dice with networks and books
- 2009
-
Doctoral thesis (other academic/artistic)abstract
- Complex systems are neither perfectly regular nor completely random. They consist of a multitude of players who, in many cases, playtogether in a way that makes their combined strength greater than the sum of their individual achievements. It is often very effective to represent these systems as networks where the actual connections between the players take on a crucial role.Networks exist all around us and are an important part of our world, from the protein machinery inside our cells to social interactions and man-madecommunication systems. Many of these systems have developed over a long period of time and are constantly undergoing changes driven by complicated microscopic events. These events are often too complicated for us to accurately resolve, making the world seem random and unpredictable. There are however ways of using this unpredictability in our favor by replacing the true events by much simpler stochastic rules giving effectively the same outcome. This allows us to capture the macroscopic behavior of the system, to extract important information about the dynamics of the system and learn about the reason for what we observe. Statistical mechanics gives the tools to deal with such large systems driven by underlying random processes under various external constraints, much like how intracellular networks are driven by random mutations under the constraint of natural selection.This similarity makes it interesting to combine the two and to apply some of the tools provided by statistical mechanics on biological systems.In this thesis, several null models are presented, with this view point in mind, to capture and explain different types of structural properties of real biological networks. The most recent major transition in evolution is the development of language, both spoken and written. This thesis also brings up the subject of quantitative linguistics from the eyes of a physicist, here called linguaphysics. Also in this case the data is analyzed with an assumption of an underlying randomness. It is shown that some statistical properties of books, previously thought to be universal, turn out to exhibit author specific size dependencies. A meta book theory is put forward which explains this dependency by describing the writing of a text as pulling a section out of a huge, individual, abstract mother book.
|
|
