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A simple three protein negative feedback loop modeled with mass action kinetic differential equations. Each protein interaction is described by a Michealis Menten reaction.

A simple three protein negative feedback loop modeled with mass action kinetic differential equations. Each protein interaction is described by a Michealis Menten reaction.

Researchers begin by choosing a biological pathway and diagramming all of the protein interactions. After determining all of the interactions of the proteins, [[mass action kinetics]] is utilized to describe the speed of the reactions in the system. Mass action kinetics will provide differential equations to model the biological system as a mathematical model in which experiments can determine the parameter values to use in the [[differential equation]]s.<ref>{{Cite journal|last=Chellaboina|first=V.|last2=Bhat|first2=S. P.|last3=Haddad|first3=W. M.|last4=Bernstein|first4=D. S.|date=August 2009|title=Modeling and analysis of mass-action kinetics|journal=IEEE Control Systems Magazine|volume=29|issue=4|pages=60–78|doi=10.1109/MCS.2009.932926|issn=1941-000X}}</ref> These parameter values will be the reaction rates of each proteins interaction in the system. This model determines the behavior of certain proteins in biological systems and bring new insight to the specific activities of individual proteins. Sometimes it is not possible to gather all reaction rates of a system. Unknown reaction rates are determined by simulating the model of known parameters and target behavior which provides possible parameter values.<ref>{{Cite journal|last=Brown|first=Kevin S.|last2=Sethna|first2=James P.|date=2003-08-12|title=Statistical mechanical approaches to models with many poorly known parameters|journal=Physical Review E|volume=68|issue=2|pages=021904|doi=10.1103/physreve.68.021904|pmid=14525003|bibcode=2003PhRvE..68b1904B|issn=1063-651X}}</ref><ref name=":03" />

Researchers begin by choosing a biological pathway and diagramming all of the protein interactions. After determining all of the interactions of the proteins, [[mass action kinetics]] is utilized to describe the speed of the reactions in the system. Mass action kinetics will provide differential equations to model the biological system as a mathematical model in which experiments can determine the parameter values to use in the [[differential equation]]s.<ref>{{Cite journal|last=Chellaboina|first=V.|last2=Bhat|first2=S. P.|last3=Haddad|first3=W. M.|last4=Bernstein|first4=D. S.|date=August 2009|title=Modeling and analysis of mass-action kinetics|journal=IEEE Control Systems Magazine|volume=29|issue=4|pages=60–78|doi=10.1109/MCS.2009.932926|issn=1941-000X}}</ref> These parameter values will be the reaction rates of each proteins interaction in the system. This model determines the behavior of certain proteins in biological systems and bring new insight to the specific activities of individual proteins. Sometimes it is not possible to gather all reaction rates of a system. Unknown reaction rates are determined by simulating the model of known parameters and target behavior which provides possible parameter values.<ref>{{Cite journal|last=Brown|first=Kevin S.|last2=Sethna|first2=James P.|date=2003-08-12|title=Statistical mechanical approaches to models with many poorly known parameters|journal=Physical Review E|volume=68|issue=2|pages=021904|doi=10.1103/physreve.68.021904|pmid=14525003|bibcode=2003PhRvE..68b1904B|issn=1063-651X}}</ref><ref name=":03" />

Researchers begin by choosing a biological pathway and diagramming all of the protein interactions. After determining all of the interactions of the proteins, mass action kinetics is utilized to describe the speed of the reactions in the system. Mass action kinetics will provide differential equations to model the biological system as a mathematical model in which experiments can determine the parameter values to use in the differential equations. These parameter values will be the reaction rates of each proteins interaction in the system. This model determines the behavior of certain proteins in biological systems and bring new insight to the specific activities of individual proteins. Sometimes it is not possible to gather all reaction rates of a system. Unknown reaction rates are determined by simulating the model of known parameters and target behavior which provides possible parameter values.

Researchers begin by choosing a biological pathway and diagramming all of the protein interactions. After determining all of the interactions of the proteins, mass action kinetics is utilized to describe the speed of the reactions in the system. Mass action kinetics will provide differential equations to model the biological system as a mathematical model in which experiments can determine the parameter values to use in the differential equations. These parameter values will be the reaction rates of each proteins interaction in the system. This model determines the behavior of certain proteins in biological systems and bring new insight to the specific activities of individual proteins. Sometimes it is not possible to gather all reaction rates of a system. Unknown reaction rates are determined by simulating the model of known parameters and target behavior which provides possible parameter values.

[[File:Toy_Model_Plot.jpg|thumb|325x325px|Plot of Concentrations vs time for the simple three protein negative feedback loop. All parameters are set to either 0 or 1 for initial conditions. The reaction is allowed to proceed until it hits equilibrium. This plot is of the change in each protein over time.]]

[[File:Toy_Model_Plot.jpg|thumb|325x325px|Plot of Concentrations vs time for the simple three protein negative feedback loop. All parameters are set to either 0 or 1 for initial conditions. The reaction is allowed to proceed until it hits equilibrium. This plot is of the change in each protein over time.]]

Plot of Concentrations vs time for the simple three protein negative feedback loop. All parameters are set to either 0 or 1 for initial conditions. The reaction is allowed to proceed until it hits equilibrium. This plot is of the change in each protein over time.

Plot of Concentrations vs time for the simple three protein negative feedback loop. All parameters are set to either 0 or 1 for initial conditions. The reaction is allowed to proceed until it hits equilibrium. This plot is of the change in each protein over time.

 

 

== See also ==

== See also ==