A novel approach to model neuronal signal transduction using stochastic differential equations

We introduce a new approach to model the behavior of neuronal signal transduction networks using stochastic differential equations. We present first a mathematical formulation for a stochastic model of protein kinase C pathway. Different kinds of numerical integration methods, including the explicit and implicit Euler-Maruyama methods, are used to solve the [email protected]^ form of the stochastic model. Stochastic models may provide more realistic representations for the chemical species in signal transduction networks compared to deterministic models. Our approach has the advantage of being computationally less demanding in the context of large-scale stochastic simulations than other approaches where individual chemical interactions are simulated stochastically.

[1]  P. Smolen,et al.  Calcium dynamics in large neuronal models , 1998 .

[2]  H. Othmer,et al.  Frequency encoding in excitable systems with applications to calcium oscillations. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[4]  A. Lawrie,et al.  Synchronous calcium oscillations in cerebellar granule cells in culture mediated by NMDA receptors. , 1993, Neuroreport.

[5]  Kevin Burrage,et al.  Stochastic approaches for modelling in vivo reactions , 2004, Comput. Biol. Chem..

[6]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[7]  U. Bhalla,et al.  Emergent properties of networks of biological signaling pathways. , 1999, Science.

[8]  J. Keizer,et al.  A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[9]  B. Øksendal.  Stochastic Differential Equations , 1985 .

[10]  Upinder S. Bhalla,et al.  The Database of Quantitative Cellular Signaling: management and analysis of chemical kinetic models of signaling networks , 2003, Bioinform..

[11]  T. Bliss,et al.  A synaptic model of memory: long-term potentiation in the hippocampus , 1993, Nature.

[12]  C. Koch,et al.  Methods in Neuronal Modeling: From Ions to Networks , 1998 .