| 1. |
- Gennemark, Peter, 1974, et al.
(author)
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A simple mathematical model of adaptation to high osmolarity in yeast
- 2006
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In: In silico biology. - 1434-3207 .- 1386-6338. ; 6:0018
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Journal article (peer-reviewed)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.
(author)
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Benchmarks for identification of ordinary differential equations from time series data
- 2009
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In: Bioinformatics. - : Oxford University Press (OUP). - 1460-2059 .- 1367-4803 .- 1367-4811. ; 25:6, s. 780-786
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Journal article (peer-reviewed)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.
(author)
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Efficient algorithms for ordinary differential equation model identification of biological systems
- 2007
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In: IET Systems Biology. - 1751-8849. ; 1:2, s. 120-129
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Journal article (peer-reviewed)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.
(author)
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Improved Parameter Estimation for Completely Observed Ordinary Differential Equations with Application to Biological Systems
- 2009
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In: 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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Conference paper (peer-reviewed)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, et al.
(author)
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ODEion- a software module for structural identification of ordinary differential equations
- 2014
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In: Journal of Bioinformatics and Computational Biology. - 0219-7200 .- 1757-6334. ; 12:1
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Journal article (peer-reviewed)abstract
- In the systems biology field, algorithms for structural identification of ordinary differential equations (ODEs) have mainly focused on fixed model spaces like S-systems and/or on methods that require sufficiently good data so that derivatives can be accurately estimated. There is therefore a lack of methods and software that can handle more general models and realistic data. We present ODEion, a software module for structural identification of ODEs. Main characteristic features of the software are: • The model space is defined by arbitrary user-defined functions that can be nonlinear in both variables and parameters, such as for example chemical rate reactions. • ODEion implements computationally efficient algorithms that have been shown to efficiently handle sparse and noisy data. It can run a range of realistic problems that previously required a supercomputer. • ODEion is easy to use and provides SBML output. We describe the mathematical problem, the ODEion system itself, and provide several examples of how the system can be used. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219720013500157
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| 7. |
- Jahan, Tabassum, 1984, et al.
(author)
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Evaluating the design of a course in mathematical modelling and problem solving
- 2016
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In: Proceedings - The 18th SEFI Mathematics Working Group seminar on Mathematics in Engineering Education. ; , s. 111-116
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Conference paper (peer-reviewed)abstract
- Mathematical modelling and problem solving constitute central aspects of everyday engineering work. But how can we design courses that help students develop these key skills? In this paper we describe the design and evaluation of an inquiry-based course in mathematical modelling and problem solving for second-year engineering students. The course was evaluated using a qualitative research approach based on reflective reports submitted by the students at the end of the course. The students report a significant development in their mathematical modelling and problem solving skills, including metacognitive skills, and their belief system. The authentic learning environment contributed to these learning outcomes. The problems in conjunction with several other aspects of the course created this authentic environment. We discuss a framework for designing authentic learning environments and its significance for engineering education.
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| 8. |
- Kattas, G.D., et al.
(author)
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Structural identification of GMA models: Algorithm and model comparison
- 2010
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In: CMSB 2010 - Proceedings of the 8th International Conference on Computational Methods in Systems Biology. - New York, NY, USA : ACM. - 9781450300681 ; , s. 107-113
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Conference paper (peer-reviewed)abstract
- We propose a local search algorithm for structural identification of Generalized Mass Action (GMA) models from time course data. The algorithm has been implemented as part of our existing system for identification of dynamical systems. We compare this approach to existing alternatives in terms of analytical GMA models, analytical GMA models with parameter estimation from time course data, S-systems, and linear models. This is done on three new test problems designed to exhibit different characteristic properties of biochemical pathways, and which are defined with chemical rate reactions. By applying state-of-the-art algorithmic methods we are able to make a full investigation for the test problems also with noisy data. The results show that on the tested problems, our structural identification algorithm is able to find as good or better models than any of the other approaches. It can therefore be expected to be a useful tool for identifying models of unknown systems from time course data. All test problems are available on the web. Copyright 2010 ACM.
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