"
Team:NTU-Taida/Modeling/Stochastic Modeling
From 2013.igem.org
(Created page with "{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=Introduction to Stochastic Modeling}}{{:Team:NTU-Taida/Templates...") |
|||
| Line 3: | Line 3: | ||
As we know, deterministic model for a biology system uses sets of ODEs (ordinary differential equation) to describe the system dynamic behaviour. These differential equation are treated under continuous manner, which is a approximation of large quantity of molecule number in the environment. Moreover, following the theory that each reaction is the collision with proper direction and energy of molecules, we can assume the molecules are spread uniformly about the environment and each reaction rate can be evaluated by classical chemical kinetic law. However, such assumption failed if molecule number is few. | As we know, deterministic model for a biology system uses sets of ODEs (ordinary differential equation) to describe the system dynamic behaviour. These differential equation are treated under continuous manner, which is a approximation of large quantity of molecule number in the environment. Moreover, following the theory that each reaction is the collision with proper direction and energy of molecules, we can assume the molecules are spread uniformly about the environment and each reaction rate can be evaluated by classical chemical kinetic law. However, such assumption failed if molecule number is few. | ||
| - | When the molecule number is few, the effect of probability emerges. We should consider the probability of every effective collision. In this model, we define that a | + | When the molecule number is few, the effect of probability emerges. We should consider the probability of every effective collision. In this model, we define that a '''state''' is one or more species with a particular number of molecule for each species. Each reaction involves at most two molecules as reactant. The reactions lead to '''state transitions'''. Take our model into consideration. The species involving in this model are: |
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Human Practice}} | {{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Human Practice}} | ||
Revision as of 12:34, 27 September 2013
Introduction to Stochastic Modeling
As we know, deterministic model for a biology system uses sets of ODEs (ordinary differential equation) to describe the system dynamic behaviour. These differential equation are treated under continuous manner, which is a approximation of large quantity of molecule number in the environment. Moreover, following the theory that each reaction is the collision with proper direction and energy of molecules, we can assume the molecules are spread uniformly about the environment and each reaction rate can be evaluated by classical chemical kinetic law. However, such assumption failed if molecule number is few.
When the molecule number is few, the effect of probability emerges. We should consider the probability of every effective collision. In this model, we define that a state is one or more species with a particular number of molecule for each species. Each reaction involves at most two molecules as reactant. The reactions lead to state transitions. Take our model into consideration. The species involving in this model are:
