@article{(Open Science Index):https://publications.waset.org/pdf/5322,
	  title     = {A Computational Stochastic Modeling Formalism for Biological Networks},
	  author    = {Werner Sandmann and  Verena Wolf},
	  country	= {},
	  institution	= {},
	  abstract     = {Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.
},
	    journal   = {International Journal of Computer and Information Engineering},
	  volume    = {2},
	  number    = {2},
	  year      = {2008},
	  pages     = {498 - 503},
	  ee        = {https://publications.waset.org/pdf/5322},
	  url   	= {https://publications.waset.org/vol/14},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 14, 2008},
	}