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Team:University of Ottawa/Modeling
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Parameters | Parameters | ||
The values for the parameters governing expression of the core signaling components (IP, CRE1, YPD1, SKN7) were taken from the model of Chen and Weiss []. The parameters specific to our system were either gleaned from other sources if available, or were varied within reasonable ranges to explore their effect on the dynamics of the system. | The values for the parameters governing expression of the core signaling components (IP, CRE1, YPD1, SKN7) were taken from the model of Chen and Weiss []. The parameters specific to our system were either gleaned from other sources if available, or were varied within reasonable ranges to explore their effect on the dynamics of the system. | ||
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| + | =Receiver cells= | ||
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| + | N, M and IP are total culture variables. Cell density (N, M) is modeled as logistic growth, with carrying capacity Nmax, Mmax. Continuous culture dilution may be chosen rather than batch culture by setting a nonzero dilution rate (kdil). Inducer concentration (IP) in the reactor is affected by an overall degradation rate (kdip), the culture dilution rate (kdil), and binding/releasing of the molecule to the receptor in both its phosphorylated (CRE1p) and non-phosphorylated (CRE1) state. IP is assumed to diffuse rapidly across the cell membrane so that intracellular and total culture IP concentrations are the same at all times. The effective “receptor concentration” in the total reactor volume (mol receptors/culture volume) is estimated by multiplying the cellular concentration of receptors (mol receptors per cell/cell volume) by the cell density times cell volume. Simple Michaelis-Menten kinetics is used to model enzyme-mediated degradation of IP by CKX. With these assumptions, we derive the differential equations below. | ||
Revision as of 10:31, 27 October 2008
Modeling
Variables Our models contain the following variables and species:
Reactions
Parameters The values for the parameters governing expression of the core signaling components (IP, CRE1, YPD1, SKN7) were taken from the model of Chen and Weiss []. The parameters specific to our system were either gleaned from other sources if available, or were varied within reasonable ranges to explore their effect on the dynamics of the system.
Receiver cells
N, M and IP are total culture variables. Cell density (N, M) is modeled as logistic growth, with carrying capacity Nmax, Mmax. Continuous culture dilution may be chosen rather than batch culture by setting a nonzero dilution rate (kdil). Inducer concentration (IP) in the reactor is affected by an overall degradation rate (kdip), the culture dilution rate (kdil), and binding/releasing of the molecule to the receptor in both its phosphorylated (CRE1p) and non-phosphorylated (CRE1) state. IP is assumed to diffuse rapidly across the cell membrane so that intracellular and total culture IP concentrations are the same at all times. The effective “receptor concentration” in the total reactor volume (mol receptors/culture volume) is estimated by multiplying the cellular concentration of receptors (mol receptors per cell/cell volume) by the cell density times cell volume. Simple Michaelis-Menten kinetics is used to model enzyme-mediated degradation of IP by CKX. With these assumptions, we derive the differential equations below.
