On the Mathematical Structure and Algorithmic Implementation of Biochemical Network Models
Creators
Description
Modeling and simulation of biochemical reactions is of great interest in the context of system biology. The central dogma of this re-emerging area states that it is system dynamics and organizing principles of complex biological phenomena that give rise to functioning and function of cells. Cell functions, such as growth, division, differentiation and apoptosis are temporal processes, that can be understood if they are treated as dynamic systems. System biology focuses on an understanding of functional activity from a system-wide perspective and, consequently, it is defined by two hey questions: (i) how do the components within a cell interact, so as to bring about its structure and functioning? (ii) How do cells interact, so as to develop and maintain higher levels of organization and functions? In recent years, wet-lab biologists embraced mathematical modeling and simulation as two essential means toward answering the above questions. The credo of dynamics system theory is that the behavior of a biological system is given by the temporal evolution of its state. Our understanding of the time behavior of a biological system can be measured by the extent to which a simulation mimics the real behavior of that system. Deviations of a simulation indicate either limitations or errors in our knowledge. The aim of this paper is to summarize and review the main conceptual frameworks in which models of biochemical networks can be developed. In particular, we review the stochastic molecular modelling approaches, by reporting the principal conceptualizations suggested by A. A. Markov, P. Langevin, A. Fokker, M. Planck, D. T. Gillespie, N. G. van Kampfen, and recently by D. Wilkinson, O. Wolkenhauer, P. S. Jöberg and by the author.
Files
13372.pdf
Files
(328.6 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:517e3bb85cb00cee9bc8055b651d37cf
|
328.6 kB | Preview Download |
Additional details
References
- R. Alur, C. Belta, F. Ivancic, V. Kumar, M. Mintz, G. Pappas, H. Rubin, and J. Schug. Hybrid modeling and simulation of biomolecular networks. In Hybrid System. Computation and Control, 4th International Workshop, HSCC, Rome Italy, 2001.
- T. M. Bartol and J. R. Stiles. M-cell, http://www.MCell.cnl.salk.edu, 2002.
- A. Bockmayr and A. Courtois. Using hydrid concurrent programming to model dynamics biological systems. In 18th International Conference on Logic Programming, ICLP02, pages 85-99. Springer, LNCS 2401, July 2002.
- J. Elf, A. Doncic, and M. Eherenberg. Mesoscopic reaction-diffusion in intracellular signaling. In Proceedings of SPIE 5110, pages 114-124, 2003.
- P. Erdi and G. Barna. Self-organisation in neural systems. some illustrations. Lecture Notes in Bioinformatics, 71, 1993.
- B. Ermentrout. Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. 1st edition. SIAM New York, 2002.
- M. Gibson and J. Bruck. Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A, 104, 2000.
- D. T. Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical species. J.Comp. Physics, 22:403-434, 1976.
- D. T. GIllespie. Exact stochastic simulation of coupled chemical reactions. The J. of Physical Chemistry, 81(25), 1977. [10] D. T. Gillespie. Markov Processes. Academic Press, 1992. [11] D. T. GIllespie. A rigorous derivation of the chemical master equation. Physica A, 188:404-425, 1992. [12] D. T. Gillespie. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys., 115:1716-1733, 2001. [13] E. L. Haseltine and J. B. Rawlings. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys., 117:6959-6969, 2002. [14] J. Hasty and F. Issacs. Designer gene networks: toward fundamental cellular control. CHAOS, 11(1):207-220, 2001. [15] W. Horsthemke and L. Hanson. Non equilibrium chemical instabilities in continuous flow stirred tank reactors: the effect of stirring. J. Chem. Phys., 81, 1993. [16] P. S. J┬¿oberg. Numerical solution of the Fokker-Planck approximation of the chemical master equation. Master-s thesis, Dept. of Information Technology, Uppsala University, 2005. [17] T. R. Kiehl, R. M. Mattheyses, and M. K. Simmons. Hybrid simulation of cellular behavior. Bioinformatics, 20:316-322, 2004. [18] P. Lecca. Simulating the cellular passive transport of glucose using a time-dependent extension of gillespie algorithm for stochastic ¤Ç - calculus. Int. Journal of Data Mining and Bioinformatics, 1(4), 2006. [19] P. Lecca. A time-dependent extension of gillespie algorithm for biochemical stochastic ¤Ç-calculus. In SAC ACM -06, 2006. [20] P. Lecca and L. Dematt`e. Stochastic simulation of reaction diffusion systems. In. Journal of Medical and Biological Engineering, 1(4):211- 231, 2008. [21] P. Lecca, L. Dematt`e, and C. Priami. Modeling and simulating reactiondiffusion systems with state-dependent diffusion coefficients. In Int. Conference on Bioinformatics and Biomedicine 2008, volume 34. World Academy of Science, Engineering and Technology. [22] T. Lu., L. Tsimring D. Volfson, and J. Hasty. Cellular growth and division in the gillespie algorithm. Syst. Biol., 1, 2004. [23] C. M. maclan. Model verification and validation. In Workshop on "Threat Anticipation: Social Science Methods and Models", The University of Chicago and Argonne National Laboratory. [24] H. Matsuno, A. Doj, M. Nagasaki, and S. Miyano. Hybrid petri net representations of gene regulatory networks. In Pac. Symp. Biocomput., pages (5) -333-349, 2000. [25] D. A. McQuarrie. Stochastic approach to chemical kinetics. J. Appl. Prob., 4:413-478, 1967. [26] W. Kolch O. Wolkenhauer, M. Ullah and K. Cho. Modelling and simulation of intracellular dynamics: Choosing an appropriate framework. IEEE Transaction on Nano-Bioscience, Special Issue molecular and subcellular system biology, 2004. [27] J. Puchalka and A. M. Kierzek. Binding the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys. J., 86:1357-1372, 2004. [28] F. Hayot R. Bundschuh and C. Javaprakash. Fluctuations of slow variables in generic netwroks. Biophys. J., 84:1606-1615, 2003. [29] R. G. Sargent. Simulation model verification and validation. In Proceedings of the 23rd conference on Winter simulation, pages 37- 47. IEEE Computer Society Washington, DC, USA. [30] T. S. Shimizu. The spatial organisation of cell signaling pathways - a computer based study. PhD thesis, University of Cambridge, UK, 2002. [31] A. B. Stundzia and C. J. Lumsden. Stochastic simulation of coupled reaction-diffusion processes. J. Comput. Phys., 127:196-207, 1996. [32] N. G. van Kampfen. Stochastic Processes in Physics and Chemistry. Elsevier, Amsterdam, 1992. [33] D. J. Wilkinson. Stochastic Modeling for System Biology. Chapman & Hall, 2006.