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BIOINFORMATICS APPLICATIONS NOTE Vol. 18 no. 0 2002 Pages 1–2 Genexp—a genetic network simulation environment Tra Thi Vu and Jiri Vohradsky ∗ Institute of Microbiology, CAS, Videnska 1083, 142 20 Prague, Czech Republic Received on February 5, 2002; revised on March 27, 2002; accepted on April 26, 2002 ABSTRACT Summary: An environment for simulation of dynamics of genetic regulatory networks is presented. The model is based on the recurrent neural network principle and allows to interactively simulate various genetic regulatory interactions under different features of the system. The results are displayed graphically. Availability: http://proteom.biomed.cas.cz/genexp Contact: [email protected] INTRODUCTION The vast quantity of data generated by genomic expression arrays affords researchers a significant opportunity to transform biology, medicine, and pharmacology using systematic computational methods. The availability of transcriptomic (and eventually proteomic) expression data promises to have a profound impact on the understanding of basic cellular processes, the diagnosis and treatment of disease, and the efficacy of designing and delivering targeted therapeutics. Particularly relevant to these objectives is the development of a deeper understanding of the various mechanisms by which cells control and regulate the transcription of their genes by their mathematical representation. Several approaches to the modeling of cell regulatory pathways have been published recently. Those based on recurrent neural networks (Vohradsky, 2001a,b; Marnellos and Mjolsness, 1998; Marnellos et al., 2000) have been shown to be potentially very useful. The regulatory process is considered as the combinatorial action of gene products on the rate of expression of a particular gene. The action is modulated by a particular transfer function to generate response curves, which correspond to those observed in natural processes. The accumulation of gene product, controlled by the regulators, is modified by the degradation, which is usually presented as a first order chemical reaction. Such models proved to be capable of describing known, already quite complex, systems; moreover it was capable of predicting the behavior of the system in experimentally inaccessible situations ∗ To whom the correspondence should be addressed. c Oxford University Press 2002 (Vohradsky, 2001a,b). This implies that having a tool which would allow the simulation of the dynamic behavior of a genetic network under different conditions would be useful for the analysis of such systems. In this paper, we present a program based on this concept, which allows to simulate the process of gene expression of a complex regulatory network. The model allows users to compute and display time series of the amounts of the gene products involved in a specified regulatory process under various combinations of parameters. THE MODEL The principle has been published previously (Vohradsky, 2001a,b). Here we will only briefly mention the fundamentals of the algorithm. Let assume that the modeled regulatory system S is formed by n genes (nodes of the network), which can control each other including itself. The level of regulatory influence of a particular gene product i on a gene j is given by a weight wi j . All the weights form the weight matrix: W = (wi j )nxn , i = 1, . . . , n j = 1, . . . , n (1) Nonzero values define connections between nodes of the network. Applying the regulatory effect on each gene for all nodes of the system S, the regulatory effect can be defined as: gi = 1 , 1 + exp − j wi j y j − bi i = 1, . . . , n (2) where bias bi represents an external input, in this case translated as a reaction delay parameter, and yi j are concentrations of gene products of the system. Equation (2) describes the regulatory effect on gene i transformed by a sigmoidal function to the interval 0, 1. The rate of expression of a target gene i (dyi /dt) is then given by the formula: dyi = k1i gi − k2i yi dt (3) 1 T.T.Vu and J.Vohradsky where k1i and k2i are gene product i accumulation and degradation rate constants respectively. The decay rate constant k2 can be expressed using protein half-life t1/2 by the formula: k2 = ln 2/t1/2 (4) The whole model is formed by a set of differential equations: 1 dyi = k1i dt 1 + exp − j wi j yi − bi −(ln 2/t1/2i )yi , i = 1, . . . , n. (5) The changes in the accumulation of a gene product is computed using modified Runge–Kutta method as implemented in MATLAB ‘ode45’ function. IMPLEMENTATION OF THE MODEL The free parameters of the model, which are user defined, are: connection weight matrix: maximal rate of expression (accumulation rate constant) vector: vector of protein half lifes: delay parameters vector: initial level of expression vector: W = (wi j )nxn k1 = (k1i ); i = 1, . . . , n t1/2 = (t1/2i ); i = 1, . . . , n b = (bi ); i = 1, . . . , n y0 = (y0i ); i = 1, . . . , n The number n of nodes (genes) involved in the regulatory process defines the dimension of the matrix and the length of the vectors. The program communicates with the user by means of five windows, which are classified into two parts: The input includes the Gene-Expression window (GE), the Edit-Data window (ED) and Notepad window (NP); and the output includes the Select-Node window (SN) and the Plot-of-Model window (PM). To start a simulation loop, the user can choose either to edit an existing data file or to create a new one. If number of genes of the system is lower than 15 a special editor is invoked, if higher the data are edited in NOTEPAD. The Edit-Data window (ED) is used to edit parameters of the model (mentioned above). After editing the current data are checked for consistency, and the SN and PM windows are opened. There user can select which kinetic profiles to plot in the PM window, and for what time interval. The PLOT button in SN invokes the simulation procedure, which uses the currently edited data and displays resulting curves in the PM window. CONCLUSIONS Here we present a user friendly program, based on a neural network model of gene expression, which allows the behavior of arbitrarily designed genetic regulatory network for different parameters and time intervals to be 2 simulated, especially how the system would be affected if some of its parts were influenced by an outside action, such as the change in protein stability or activity, or e.g. by gene disruption. It can be useful for the analysis of a studied network or for planning experiments, which would confirm or reject suggested or expected network topology i.e. the regulatory interaction among genes of the system. The program was designed and tested for various x86 processors and different MS Windows versions. It can run either as a stand-alone compiled application under MS Windows environment or in MATLAB using a set of scripts. All scripts and compiled version for Matlab 6.1 and MS Windows environment, together with installer and help files, are freely available at the above-mentioned address. ACKNOWLEDGEMENTS The authors wish to thank Jeremy Ramsden for discussion and comments on the manuscript. The work was supported by grants of GACR No. 204/00/1253 and GACAS No. GA204/02/1452. REFERENCES Marnellos,G. and Mjolsness,E. (1998) A gene network approach to modeling early neurogenesis in Drosophila. Pac. Symp. Biocomput., 30–41. Marnellos,G., Deblandre,G.A., Mjolsness,E. and Kintner,C. (2000) Delta-Notch lateral inhibitory patterning in the emergence of ciliated cells in Xenopus: experimental observations and a gene network model. Pac. Symp. Biocomput., 329–340. Vohradsky,J. (2001a) Neural model of the genetic network. J. Biol. Chem., 276, 36168–36173. Vohradsky,J. (2001b) Neural network model of gene expression. Faseb J., 15, 846–854. To be balanced at final stage