Hybrid Modeling in Computational Neuropsychiatry

Abstract

The aim of building mathematical models is to provide a formal structure to explain the behaviour of a whole in terms of its parts. In the particular case of neuropsychiatry, the available information upon which models are to be built is distributed over several fields of expertise. Molecular and cellular biologists, physiologists and clinicians all hold valuable information about the system which has to be distilled into a unified view. Furthermore, modelling is not a sequential process in which the roles of field and modelling experts are separated. Model building is done through iterations in which all the parts have to keep an active role. This work presents some modelling techniques and guidelines on how they can be combined in order to simplify modelling efforts in neuropsychiatry. The proposed approach involves two well known modelling techniques, Petri nets and Biochemical System Theory that provide a general well proven structured definition for biological models.

References

• 1 Alla H, Cavaille J-B, Le Bail J, Bel G. , “Les systèmes de production par lot: une approche discret-continu utilisant les réseaux de Petri hybrids,” Proc. of 1st Int. Conf. on Automation of Mixed Processes (Paris, France), January 1992
• 2 Bender W, Albus M, Müller HJ, Tretter F. Towards systemic theories in biological psychiatry.  Pharmacopsychiatry. 2006;  39 ((S1)) S4-S9
• 3 Drath R. Hybrid object nets: An object oriented concept for modeling complex hybrid systems.  Proc Hybrid Dynamical Systems, 3rd International Conference on Automation of Mixed Processes ADPM’98. 1998;  437-442
• 4 Gilbert D, Heiner M, Lehrack S. , A Unifying Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets, BTU Cottbus ComputerScience Reports (2007), Report 02/07
• 5 Gonzalez O, Gronau S, Falb M, Pfeiffer F, Mendoza E, Zimmer R, Oesterhelt D. Reconstruction, modeling & analysis of Halobacterium salinarum R-1 metabolism.  Molecular Biosystems. 2008;  4 148-159
• 6 Matsuno H, Tanaka Y, Aoshima H, Doi A, Matsui M, Miyano S. Biopathways representation and simulation on hybrid functional.  Petri net In Silico Biology. 2003;  3 0032
• 7 Peng SC, Chang H-M, Hsu DF, Tang CY. Modeling signal transduction of neural system by hybrid petri net representation.  Operations Research Proceedings 2004, Part 9. 2005;  271-279
• 8 Reddy VN, Mavrovouniotis ML, Liebman MN. Petri net representations in metabolic pathways.  Proceedings of the International Conference on Intelligent Systems in Molecular Biology. 1993;  1 328-336
• 9 Rodriguez EM, del Rosario RCH, Rudy A, Vollmar A, Mendoza ER. A discrete Petri Net model for cephalostatin 1-induced apoptosis in leukemic cells, submitted to Natural Computing. 2008; 
• 10 Sackmann A, Heiner M, Koch I. Application of Petri net based analysis techniques to signal transduction pathways.  BMC Bioinformatics. 2006;  7 482
• 11 Shiraishi F, Savageau MA. The Tricarboylic Acid Cycle in Dictyostelium discoideum 1 Formulation of alternative kinetic representations.  Journal of Biological Chemistry. 1992;  267 ((32)) 22912-22918
• 12 Voit EO. Computational Analysis of Biochemical Networks. Cambridge University Press 2000
• 13 Wu J, Voit EO. Extending Biochemical Systems Theory to Hybrid Modeling by Means of Functional Petri Nets, Poster presented at the 10th International Conference on Molecular Systems Biology. Manila, Philippines 2008

Correspondence