Team:UFlorida/Model
Project Model
Genetic Inverter Description
The genetic inverter utilizes a repressible, repressor sequence (TetR) paired with a downstream, complementary, and constitutively expressed, but repressible promoter sequence (pTet). Both sequences are downstream of a constructively promoted, but repressible promoter sequence (pPhoA). At high levels of inorganic phosphorus, a cell will produce a phosphorylated form of the PhoB protein which will in turn repress the expression of pPhoA (and subsequently TetR) which will allow for expression of pTet.
Xm: The concentration of mRNA of species X at a given time point.
Xp: The concentration of protein of species X at a given time point.
Xp!: The concentration of the phosphorylated form of protein of species X at a given time point.
kY: The rate of phrase Y in the subscript.
βZ: The maximal transcription rate of promoter species Z
K: Activation coefficient
N: Cooperativity
Begin PhoB-PhoR Pathway
The above equations represent the rate of change of PhoB and PhoR mRNA over time. To represent mRNA production, the maximal transcription rate of the pPhoB promoter is multiplied by an activation Hill equation which treats phosphorylated PhoB protein as the activator molecule. To represent molecular degradation, the equations then subtract the degradation rate of the respective mRNA species with the cocnetentaraion of that mRNA species at a given time.
Above are the equations for the changes in concentration over time for PhoB and PhoR proteins. To account for protein production, for both protein species the translational rate of respective mRNA species are multiplied by the concentration of mRNA at any given time. Accounting for degradation, the degradation rate for both species is multiplied by the concentration of their respective proteins at a given time. To account for phosphorylation dynamics in PhoR, the rate of binding between inorganic phosphate (Pi) is multiplied by the concentration of inorganic phosphate and the concentration of PhoR protein and subtracted from the overall equation, while the rate of inactivation of Phosphorylated PhoB protein is multiplied by the concentration of Phosphorylated PhoR protein and the concentration of PhoB protein, all of which is added to the overall equation. To account for the effects of phosphorylation on PhoB protein the activation rate of PhoB protein by phosphorylated PhoR protein is multiplied by the amount of phosphorylated PhoR protein and subtracted from the overall equation. Similarly, the rate of auto-inactivation of phosphorylated PhoB protein is multiplied by the concentration of phosphorylated PhoB protein and added to the overall equation.
For the phosphorylated forms of the PhoB and PhoR proteins, the activation rate of PhoB protein by phosphorylated PhoR protein is multiplied by the concentration of PhoB protein and phosphorylated PhoR protein at a given time point. The rate of auto-inactivation of phosphorylated PhoB protein is then multiplied by the amount of phosphorylated PhoB protein and the resulting value is subtracted from the overall equation. Similarly for the change of phosphorylated PhoR protein over time, the values for the rate of activation of PhoB protein by PhoR protein is multiplied by the concentration of PhoB protein and phosphorylated PhoR protein and the rate of unbinding of inorganic phosphorus from phosphorylated PhoR protein which is multiplied by the concentration of phosphorylated PhoB protein at a given time are both subtracted from the value of binding of inorganic phosphate multiplied by the concentration of inorganic phosphate and the concentration of PhoR protein.
End PhoB-PhoR Pathway
Begin Genetic Inverter
The “Genetic Inverter” part relies primarily on the TetR repressor sequence. The dynamics of the TetR repressor sequence are governed by an activation Hill function with phosphorylated PhoB protein is the activator molecule. The maximal transcription rate of the promoter is multiplied by the aforementioned Hill function. Afterwards the degradation rate of TetR mRNA is then multiplied by the concentration of TetR mRNA at a given time point. For the change in TetR protein over time the translation rate of TetR mRNA to TetR protein is multiplied by the concentration of TetR mRNA at a given point. The degradation rate of TetR protein is then multiplied by the concentration of TetR protein at a given point and the resulting value is subtracted from the overall equation.
End Genetic Inverter
Begin SCRIBE
All of the mRNA species above are regulated by the pTet promoter and the genetic inverter part segment. A repressor Hill function is included utilizing TetR protein as the regulatory module. The maximal transcription rate of the pTet promoter is multiplied by the aforementioned hill function. The degradation rate of each mRNA species is then multiplied then by the concentration of a respective mRNA species at a given time and the resulting value is then subtracted from the overall equation.
All of the above protein species are governed by simple translation/degradation dynamics. The respective translation rates of the species in the subscript are multiplied by the amount of their respective mRNA species. Similarly the degradation rates of the protein species in the subscript are multiplied by the concentration of their respective protein species at a given time point.
End Scribe
Assumptions, Limitations, and Future Work
Our model presupposes two major assumptions:
1.) All SCRIBE dynamics are functionally identical and reliant only on the concentrations of pTet an TetR molecules
2.) That the PhoB-PhoR phosphate starvation system can reliably be utilized to track phosphorus levels within a cellular system.
The former assumption led to us tracking TetR protein levels as opposed to SCRIBE effects on cellular biosensors, and the latter introduced a modeling error that we did not recognize until it was too late to appropriately address it. The graphs below show protein dynamic behaviors that we would not expect from a realized biosensor and that can be explained in the context of our modeling error. Our model does not take into account the complex pathway that regulates phosphate uptake within cellular systems and the inhibitory effect higher levels of phosphate have on a phosphate starvation system (the PhoB-PhoR pathway). Resultantly, our model does not track any change in TetR with relation to phosphate levels given its connection to the pPhoA promote, which does not experience any upstream inhibition from our incomplete model of PhoB and PhoR proteins. Ideally, we would see a decrease in phosphorylated PhoB protein over a certain level of inorganic phosphate and a corresponding decrease in TetR concentration. We do not observe that within our model and instead observe a phosphate independent expression of TetR protein. While introduction of inorganic phosphate to the system does induce a change in the concentration/phosphorylation of PhoB protein, the lack of an inhibitory term in our model means that we do not accurately capture realistic cellular response. Future work within this project would include capturing the inhibitory effect of high levels of inorganic phosphate on our system through a proxy constant/function derived from experimental data regarding the aforementioned complex regulatory system involved in phosphate starvation or else modeling that system in its entirety to accurately capture the effects of levels of phosphate on a system. Below are the current outputs of our model at given concentrations of phosphorous.
0 uM Pi
100 uM Pi
200 uM Pi
300 uM Pi
500 uM Pi