Modern tools for the time-discrete dynamics and optimization of gene-environment networks

Fuegenschuh, Armin
Weber, Gerhard Wilhelm
In this study, we discuss the models of genetic regulatory systems, so-called gene-environment networks. The dynamics of such kind of systems are described by a class of time-continuous ordinary differential equations having a general form (E) over dot = M(E)E, where E is a vector of gene-expression levels and environmental factors and M(E) is the matrix having functional entries containing unknown parameters to be optimized. Accordingly, time-discrete versions of that model class are studied and improved by introducing 3rd-order Heun's method and 4th-order classical Runge-Kutta method. The corresponding iteration formulas are derived and their matrix algebras are obtained. After that, we use nonlinear mixed-integer programming for the parameter estimation in the considered model and present the solution of a constrained and regularized given mixed-integer problem as an example. By using this solution and applying both the new and existing discretization schemes, we generate corresponding time-series of gene-expressions for each method. The comparison of the experimental data and the calculated approximate results is additionally done with the help of the figures to exercise the performance of the numerical schemes on this example.


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Sarıaydın, Ayşe; Karasözen, Bülent; Jost, Jürgen; Department of Scientific Computing (2010)
Analysis of large networks in biology, science, technology and social systems have become very popular recently. These networks are mathematically represented as graphs. The task is then to extract relevant qualitative information about the empirical networks from the analysis of these graphs. It was found that a graph can be conveniently represented by the spectrum of a suitable difference operator, the normalized graph Laplacian, which underlies diffusions and random walks on graphs. When applied to large...
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Recent developments in understanding the various regulatory systems, especially the developments in biology and genomics, stimulated an interest in modelling such systems. Hybrid systems, originally developed for process control applications, provide advances in modelling such systems. A particular class of hybrid systems which are relatively simpler to analyze mathematically but still capable of demonstrating the essential features of many non-linear dynamical systems is piecewise-linear systems. Implement...
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In this study, some methodologies and a review of the recently obtained new results are presented for the problem of modeling, anticipation and forecasting of genetic regulatory systems, as complex systems. In this respect, such kind of complex systems are modeled in the dynamical sense into the two different ways, namely, by a system of ordinary differential equations (ODEs) and Gaussian graphical methods (GGM). An artificial time-course microarray dataset of a gene-network is modeled as an example by usin...
Shunting inhibitory cellular neural networks with strongly unpredictable oscillations
Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (Elsevier BV, 2020-10-01)
The paper considers a new type of solutions for shunting inhibitory cellular neural networks (SICNNs), strongly unpredictable oscillations. The conditions for the existence, uniqueness and stability of the solutions are determined. Numerical examples are given to show the feasibility of the obtained results.
On the smoothness of solutions of impulsive autonomous systems
Akhmet, Marat (Elsevier BV, 2005-01-01)
The aim of this paper is to investigate dependence of solutions on parameters for nonlinear autonomous impulsive differential equations. We will specify what continuous, differentiable and analytic dependence of solutions on parameters is, define higher order derivatives of solutions with respect to parameters and determine conditions for existence of such derivatives. The theorem of analytic dependence of solutions on parameters is proved.
Citation Formats
Ö. DEFTERLİ, A. Fuegenschuh, and G. W. Weber, “Modern tools for the time-discrete dynamics and optimization of gene-environment networks,” COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, pp. 4768–4779, 2011, Accessed: 00, 2020. [Online]. Available: