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The Propagation Approach for Computing Biochemical Reaction Networks
March-April 2013 (vol. 10 no. 2)
pp. 310-322
Thomas A. Henzinger, IST Austria, Klosterneuburg
Maria Mateescu, IST Austria, Klosterneuburg
We introduce propagation models (PMs), a formalism able to express several kinds of equations that describe the behavior of biochemical reaction networks. Furthermore, we introduce the propagation abstract data type (PADT), which separates concerns regarding different numerical algorithms for the transient analysis of biochemical reaction networks from concerns regarding their implementation, thus allowing for portable and efficient solutions. The state of a propagation abstract data type is given by a vector that assigns mass values to a set of nodes, and its $({\bf next})$ operator propagates mass values through this set of nodes. We propose an approximate implementation of the $({\bf next})$ operator, based on threshold abstraction, which propagates only "significant" mass values and thus achieves a compromise between efficiency and accuracy. Finally, we give three use cases for propagation models: the chemical master equation (CME), the reaction rate equation (RRE), and a hybrid method that combines these two equations. These three applications use propagation models in order to propagate probabilities and/or expected values and variances of the model's variables.
Index Terms:
Mathematical model,Computational modeling,Biological system modeling,Equations,Vectors,Abstracts,Numerical models,formal methods,Mathematical model,Computational modeling,Biological system modeling,Equations,Vectors,Abstracts,Numerical models,biochemical reaction networks,Chemical master equation,propagation models,abstract data type
Thomas A. Henzinger, Maria Mateescu, "The Propagation Approach for Computing Biochemical Reaction Networks," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 2, pp. 310-322, March-April 2013, doi:10.1109/TCBB.2012.91
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