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Team:Virginia/Model
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In order to develop our model, we decided on a system of nonlinear ordinary differential equations (ODEs) to describe the concentrations of arsenate (As(V)) and arsenite (As(III)). This system of nonlinear ODEs are based on the concept of mass balance. The model is divided into two compartments: intracellular and extracellular. The above schematic was used to develop the model. | In order to develop our model, we decided on a system of nonlinear ordinary differential equations (ODEs) to describe the concentrations of arsenate (As(V)) and arsenite (As(III)). This system of nonlinear ODEs are based on the concept of mass balance. The model is divided into two compartments: intracellular and extracellular. The above schematic was used to develop the model. | ||
| - | The equation below describes the first part of the model whereby extracellular arsenate concentration is determined by diffusional flux into and out of the cell. This flux is determined by the concentration gradient as reflected in the equation below. | + | The equation below describes the first part of the model whereby extracellular arsenate concentration is determined by diffusional flux into and out of the cell. This flux is determined by the concentration gradient as reflected in the equation below (the k12 terms). |
| - | The next part of the model represents the intracellular arsenate concentration. This is a function of the influx of arsenate into the cell by diffusion as well as the eflux of arsenate from the cell. Furthermore, there is a term (the kc term) which represents the conversion of arsenate into arsenite by | + | The next part of the model represents the intracellular arsenate concentration. This is a function of the influx of arsenate into the cell by diffusion as well as the eflux of arsenate from the cell (again, the k12 terms). Furthermore, there is a term (the kc term) which represents the conversion of arsenate into arsenite by ArsC reductase. |
| - | Intracellular arsenite is generated by the | + | Intracellular arsenite is generated by the ArsC reductase (again, the kc term) and is also subject to the usual diffusional flux into and out of the cell (represented by the k34 terms). Furthermore, since arsenite is so water soluble, it has a difficult time passing through the nonpolar cell membrane by simple diffusion and therefore requires the cell to actively pump the arsenite out of the cell. This is the action, indeed the purpose of the ArsB pump: to get the more soluble, and more toxic arsenite out of the cell. This action of the ArsB pump is represented by the kB term in the equation below. |
| + | Finally, | ||
| - | --[[User:Bsf2u|Bsf2u]] 00: | + | |
| + | --[[User:Bsf2u|Bsf2u]] 00:16, 22 October 2009 (UTC) | ||
Revision as of 00:16, 22 October 2009
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File:Http://people.virginia.edu/~mef3s/VGEM/Ecol nat.png
In order to develop our model, we decided on a system of nonlinear ordinary differential equations (ODEs) to describe the concentrations of arsenate (As(V)) and arsenite (As(III)). This system of nonlinear ODEs are based on the concept of mass balance. The model is divided into two compartments: intracellular and extracellular. The above schematic was used to develop the model.
The equation below describes the first part of the model whereby extracellular arsenate concentration is determined by diffusional flux into and out of the cell. This flux is determined by the concentration gradient as reflected in the equation below (the k12 terms).
The next part of the model represents the intracellular arsenate concentration. This is a function of the influx of arsenate into the cell by diffusion as well as the eflux of arsenate from the cell (again, the k12 terms). Furthermore, there is a term (the kc term) which represents the conversion of arsenate into arsenite by ArsC reductase.
Intracellular arsenite is generated by the ArsC reductase (again, the kc term) and is also subject to the usual diffusional flux into and out of the cell (represented by the k34 terms). Furthermore, since arsenite is so water soluble, it has a difficult time passing through the nonpolar cell membrane by simple diffusion and therefore requires the cell to actively pump the arsenite out of the cell. This is the action, indeed the purpose of the ArsB pump: to get the more soluble, and more toxic arsenite out of the cell. This action of the ArsB pump is represented by the kB term in the equation below.
Finally,
--Bsf2u 00:16, 22 October 2009 (UTC)
