| 1. |
|
|
| 2. |
- Cedersund, G, 1978-
(författare)
-
Elimination of the initial value parameters when identifying a system close to a Hopf bifurcation.
- 2006
-
Ingår i: IEE Proceedings - Systems Biology. - : Institution of Engineering and Technology (IET). - 1741-2471 .- 1741-248X. ; 153:6, s. 448-456
-
Tidskriftsartikel (refereegranskat)abstract
- One of the biggest problems when performing system identification of biological systems is that it is seldom possible to measure more than a small fraction of the total number of variables. If that is the case, the initial state, from where the simulation should start, has to be estimated along with the kinetic parameters appearing in the rate expressions. This is often done by introducing extra parameters, describing the initial state, and one way to eliminate them is by starting in a steady state. We report a generalisation of this approach to all systems starting on the centre manifold, close to a Hopf bifurcation. There exist biochemical systems where such data have already been collected, for example, of glycolysis in yeast. The initial value parameters are solved for in an optimisation sub-problem, for each step in the estimation of the other parameters. For systems starting in stationary oscillations, the sub-problem is solved in a straight-forward manner, without integration of the differential equations, and without the problem of local minima. This is possible because of a combination of a centre manifold and normal form reduction, which reveals the special structure of the Hopf bifurcation. The advantage of the method is demonstrated on the Brusselator.
|
|
| 3. |
- Cedersund, Gunnar, 1978-, et al.
(författare)
-
Improved parameter estimation for systems with an experimentally located Hopf bifurcation
- 2005
-
Ingår i: IEE Proceedings - Systems Biology. - : IEEE. - 1741-2471 .- 1741-248X. ; 152:3, s. 161-168
-
Tidskriftsartikel (refereegranskat)abstract
- When performing system identification, we have two sources of information: experimental data and prior knowledge. Many cell-biological systems are oscillating, and sometimes we know an input where the system reaches a Hopf bifurcation. This is the case, for example, for glycolysis in yeast cells and for the Belousov-Zhabotinsky reaction, and for both of these systems there exist significant numbers of quenching data, ideal for system identification. We present a method that includes prior knowledge of the location of a Hopf bifurcation in estimation based on time-series. The main contribution is a reformulation of the prior knowledge into the standard formulation of a constrained optimisation problem. This formulation allows for any of the standard methods to be applied, including all the theories regarding the methods properties. The reformulation is carried out through an over-parametrisation of the original problem. The over-parametrisation allows for extra constraints to be formed, and the net effect is a reduction of the search space. A method that can solve the new formulation of the problem is presented, and the advantage of adding the prior knowledge is demonstrated on the Brusselator.
|
|
| 4. |
- Schmidt, Henning, et al.
(författare)
-
Linear systems approach to analysis of complex dynamic behaviours in biochemical networks
- 2004
-
Ingår i: IEE Proceedings - Systems Biology. - : Institution of Engineering and Technology (IET). - 1741-2471 .- 1741-248X. ; 1:1, s. 149-158
-
Tidskriftsartikel (refereegranskat)abstract
- Central functions in the cell are often linked to complex dynamic behaviours, such as sustained oscillations and multistability, in a biochemical reaction network. Determination of the specific mechanisms underlying such behaviours isimportant, e.g. to determine sensitivity, robustness, and modelling requirements of given cell functions. In this work we adopt a systems approach to the analysis of complex behaviours in intracellular reaction networks, described byordinary differential equations with known kinetic parameters. We propose to decompose the overall system into a number of low complexity subsystems, and consider the importance of interactions between these in generating specific behaviours. Rather than analysing the network in a state corresponding to the complex non-linear behaviour, we move the system to the underlying unstable steady state, and focus on the mechanisms causing destabilisation of this steady state. This is motivated by the fact that all complex behaviours in unforced systems can be traced to destabilisation (bifurcation) of some steady state, andhence enables us to use tools from linear system theory to qualitatively analyse the sources of given network behaviours. One important objective of the present study is to see how far one can come with a relatively simple approach to the analysis of highly complex biochemical networks. The proposed method is demonstrated by application to a model of mitotic control in Xenopus frog eggs, and to a model of circadian oscillations in Drosophila. In both examples we are able to identify the subsystems, and the related interactions, which are instrumental in generating the observed complex non-linear behaviours.
|
|
| 5. |
|
|
