| 1. |
- Gennemark, Peter, 1974, et al.
(författare)
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A simple mathematical model of adaptation to high osmolarity in yeast
- 2006
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Ingår i: In silico biology. - 1434-3207 .- 1386-6338. ; 6:0018
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Tidskriftsartikel (refereegranskat)abstract
- We present a simple ordinary differential equation (ODE) model of the adaptive response to an osmotic shock in the yeast Saccharomyces cerevisiae. The model consists of two main components. First, a biophysical model describing how the cell volume and the turgor pressure are affected by varying extra-cellular osmolarity. The second component describes how the cell controls the biophysical system in order to keep turgor pressure, or equivalently volume, constant. This is done by adjusting the glycerol production and the glycerol outflow from the cell. The complete model consists of 4 ODEs, 3 algebraic equations and 10 parameters. The parameters are constrained from various literature sources and estimated from new and previously published absolute time series data on intra-cellular and total glycerol. The qualitative behaviour of the model has been successfully tested on data from other genetically modified strains as well as data for different input signals. Compared to a previous detailed model of osmoregulation, the main strength of our model is its lower complexity, contributing to a better understanding of osmoregulation by focusing on relationships which are obscured in the more detailed model. Besides, the low complexity makes it possible to obtain more reliable parameter estimates.
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| 2. |
- Gennemark, Peter, 1974, et al.
(författare)
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Benchmarks for identification of ordinary differential equations from time series data
- 2009
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Ingår i: Bioinformatics. - : Oxford University Press (OUP). - 1460-2059 .- 1367-4803 .- 1367-4811. ; 25:6, s. 780-786
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Tidskriftsartikel (refereegranskat)abstract
- Motivation: In recent years, the biological literature has seen a significant increase of reported methods for identifying both structure and parameters of ordinary differential equations (ODEs) from time series data. A natural way to evaluate the performance of such methods is to try them on a sufficient number of realistic test cases. However, weak practices in specifying identification problems and lack of commonly accepted benchmark problems makes it difficult to evaluate and compare different methods. Results: To enable better evaluation and comparisons between different methods, we propose how to specify identification problems as optimization problems with a model space of allowed reactions (e.g. reaction kinetics like Michaelis - Menten or S-systems), ranges for the parameters, time series data and an error function. We also define a file format for such problems. We then present a collection of more than 40 benchmark problems for ODE model identification of cellular systems. The collection includes realistic problems of different levels of difficulty w.r.t. size and quality of data. We consider both problems with simulated data from known systems, and problems with real data. Finally, we present results based on our identification algorithm for all benchmark problems. In comparison with publications on which we have based some of the benchmark problems, our approach allows all problems to be solved without the use of supercomputing.
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| 3. |
- Gennemark, Peter, 1974, et al.
(författare)
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Efficient algorithms for ordinary differential equation model identification of biological systems
- 2007
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Ingår i: IET Systems Biology. - 1751-8849. ; 1:2, s. 120-129
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Tidskriftsartikel (refereegranskat)abstract
- Algorithms for parameter estimation and model selection that identify both the structure and the parameters of an ordinary differential equation model from experimental data are presented. The work presented here focuses on the case of an unknown structure and some time course information available for every variable to be analysed, and this is exploited to make the algorithms as efficient as possible. The algorithms are designed to handle problems of realistic size, where reactions can be nonlinear in the parameters and where data can be sparse and noisy. To achieve computational efficiency, parameters are mostly estimated for one equation at a time, giving a fast and accurate parameter estimation algorithm compared with other algorithms in the literature. The model selection is done with an efficient heuristic search algorithm, where the structure is built incrementally. Two test systems are used that have previously been used to evaluate identification algorithms, a metabolic pathway and a genetic network. Both test systems were successfully identified by using a reasonable amount of simulated data. Besides, measurement noise of realistic levels can be handled. In comparison to other methods that were used for these test systems, the main strengths of the presented algorithms are that a fully specified model, and not only a structure, is identified, and that they are considerably faster compared with other identification algorithms.
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| 4. |
- Gennemark, Peter, 1974, et al.
(författare)
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Improved Parameter Estimation for Completely Observed Ordinary Differential Equations with Application to Biological Systems
- 2009
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Ingår i: LEcture Notes in Computer Science: 7th International Conference on Computational Methods in Systems Biology, CMSB 2009; Bologna; Italy; 31 August 2009 through 1 September 2009. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 1611-3349. - 9783642038440 ; LNCS 5688, s. 205-217
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Konferensbidrag (refereegranskat)abstract
- We consider parameter estimation in ordinary differential equations (ODEs) from completely observed systems, and describe an improved version of our previously reported heuristic algorithm (IET Syst. Biol., 2007). Basically, in that method, estimation based on decomposing the problem to simulation of one ODE, is followed by estimation based on simulation of all ODEs of the system. The main algorithmic improvement compared to the original version, is that we decompose not only to single ODEs, but also to arbitrary subsets of ODEs, as a complementary intermediate step. The subsets are selected based on an analysis of the interaction between the variables and possible common parameters. We evaluate our algorithm on a number of well-known hard test problems from the biological literature. The results show that our approach is more accurate and considerably faster compared to other reported methods on these problems. Additionally, we find that the algorithm scales favourably with problem size.
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| 5. |
- Gennemark, Peter, 1974
(författare)
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Modeling and identification of biological systems with emphasis on osmoregulation in yeast
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis deals with two topics in the area of systems biology. Thefirst topic, model identification, concerns the problem ofautomatically identifying a mathematical model of a biochemical systemfrom experimental data. We present algorithms for model selection andparameter estimation that identify both the structure and theparameters of a differential equation model from experimental data.The algorithms are designed to handle problems of realistic size,where reactions can be non-linear in the parameters and where data canbe sparse and noisy. To achieve computational efficiency, parametersare estimated for one equation at a time, giving a fast and accurateparameter estimation algorithm compared to other algorithms in theliterature. The model selection is done with an efficient heuristicsearch algorithm, where the structure is built incrementally. The mainstrengths of our algorithms are that a complete model, and not only astructure, is identified, and that they are considerably fastercompared to other identification algorithms.The second topic concerns mathematical modeling of osmoregulation inthe yeast \emph{Saccharomyces cerevisiae}. This system involves thebiophysical and biochemical responses of a cell when it is exposed toan osmotic shock. We present two different differential equationmodels based on experimental data of this system. The first model isa detailed model taking into account an extensive amount of moleculardetail, while the second is a simple model with less detail. Wedemonstrate that both models agree well with experimental data onwild-type cells. Moreover, the models predict the behavior of othergenetically modified strains and input signals.
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| 6. |
- Klipp, Edda, et al.
(författare)
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Integrative model of the response of yeast to osmotic shock
- 2005
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Ingår i: Nature Biotechnology. - : Springer Science and Business Media LLC. - 1087-0156 .- 1546-1696. ; 23:8
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Tidskriftsartikel (refereegranskat)abstract
- Integration of experimental studies with mathematical modeling allows insight into systems properties, prediction of perturbation effects and generation of hypotheses for further research. We present a comprehensive mathematical description of the cellular response of yeast to hyperosmotic shock. The model integrates a biochemical reaction network comprising receptor stimulation, mitogen-activated protein kinase cascade dynamics, activation of gene expression and adaptation of cellular metabolism with a thermodynamic description of volume regulation and osmotic pressure. Simulations agree well with experimental results obtained under different stress conditions or with specific mutants. The model is predictive since it suggests previously unrecognized features of the system with respect to osmolyte accumulation and feedback control, as confirmed with experiments. The mathematical description presented is a valuable tool for future studies on osmoregulation in yeast and—with appropriate modifications—other organisms. It also serves as a starting point for a comprehensive description of cellular signaling.
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| 7. |
- Kühn, Clemens, 1981, et al.
(författare)
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Formal Representation of the High Osmolarity Glycerol Pathway in Yeast
- 2009
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Ingår i: Genome informatics. International Conference on Genome Informatics. - 0919-9454. ; 22, s. 69-83
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Tidskriftsartikel (refereegranskat)abstract
- The high osmolarity glycerol (HOG) signalling system in yeast belongs to the class of Mitogen Activated Protein Kinase (MAPK) pathways that are found in all eukaryotic organisms. It includes at least three scaffold proteins that form complexes, and involves reactions that are strictly dependent on the set of species bound to a certain complex. The scaffold proteins lead to a combinatorial increase in the number of possible states. To date, representations of the HOG pathway have used simplifying assumptions to avoid this combinatorial problem. Such assumptions are hard to make and may obscure or remove essential properties of the system.This paper presents a detailed generic formal representation of the HOG system without such assumptions, showing the molecular interactions known from the literature. The model takes complexes into account, and summarises existing knowledge in an unambiguous and detailed representation. It can thus be used to anchor discussions about the HOG system. In the commonly used Systems Biology Markup Language (SBML), such a model would need to explicitly enumerate all state variables. The \emph{Kappa} modelling language which we use supports representation of complexes without such enumeration.To conclude, we compare \emph{Kappa} with a few other modelling languages and software tools that could also be used to represent and model the HOG system.
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