By Péter Érdi, Gábor Lente
This quantity reports the idea and simulation tools of stochastic kinetics through integrating ancient and up to date views, provides purposes, normally within the context of platforms biology and in addition in combustion conception. in recent times, a result of improvement in experimental recommendations, similar to optical imaging, unmarried mobilephone research, and fluorescence spectroscopy, biochemical kinetic info within unmarried residing cells have more and more been on hand. The emergence of platforms biology introduced renaissance within the software of stochastic kinetic methods.
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Extra info for Stochastic Chemical Kinetics: Theory and (Mostly) Systems Biological Applications
He has shown that the expectation of the numbers of molecules in a stochastic model is close to the corresponding quantities in the deterministic model, and the difference is proportional to the reciprocal of the square root of the number of molecules (see also ). Therefore, the relative error is small, if this number is large, otherwise it is large. He also made a series of approximations of the distributions of molecule numbers under different conditions. A direct continuation of his work can be found in .
Math Biosci 223:1–11 61. Ross J, Mazur P (1961) Some deductions from a formal statistical mechanical theory of chemical kinetics. J Chem Phys 35:19–28 62. Savageau MA (1969) Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J Theor Biol 25:365–369 63. Savageau MA (1976) Biochemical systems analysis: a study of function and design in molecular biology. Addison-Wesley, Reading 64. Savageau MA (1995) Michaelis-Menten mechanism reconsidered: implications of fractal kinetics.
The actual size of the state space is typically determined by the initial conditions. A state is impossible if it is not accessible from the initial state(s), whereas a possible state is not impossible. 0/. As the largest computational problem in CDS stochastic kinetics is posed by the typically huge number of states, it is imperative to exclude all impossible states from the state space. 3 The Standard Stochastic Model of Homogeneous Reaction Kinetics 37 Counting the number of states (denoted M ) in a finite state space is usually important, but not always essential.
Stochastic Chemical Kinetics: Theory and (Mostly) Systems Biological Applications by Péter Érdi, Gábor Lente