Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade. (English) Zbl 1165.92019
Summary: Models of chemical kinetics in which some reactions are much faster than others are often treated by a type of quasi-steady-state approximation (QSSA). The total QSSA (tQSSA) was introduced for models of Michaelis-Menten enzyme kinetics and shown to be valid over a wider parameter regime than the usual QSSA. We extend the tQSSA to the Mitogen-Activated Protein Kinase Cascade, an important signaling system in cell biochemistry. These approximations were first developed in a deterministic setting, but here we also describe how to incorporate this approximation into the discrete and stochastic framework of the Chemical Master Equation (CME). The CME gives rise to a large-scale matrix exponential that can be solved by Krylov methods in combination with operator splitting and the tQSSA.
MSC:
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
Software:
ExpokitReferences:
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