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Team:Tsinghua/Modeling
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Introduction
Phage production in E.coli
Naked Plasmid Vector Production
One of our team's sub project is the use nakes plasmid binded with a specified protein as the vector of gene therapy DNA. The normal replication process of plasmid will be changed due to the binding of specified protein(in our model,lambda repressor). Considering production of the plasmid protein complex, we want to maxize the amounts of plasmid protein complex, so a balance between the amounts of plasmid and protein is needed. In this model, we want to find out the optimized parameters for this plasmid vector production process.
Reaction kinetics
Dimmer formation and dissociation between λ cI repressor protein
parameters:
kdon =0.05/(M*sec) (Burz et al. (1994); Shea and Ackers (1985) ) kdoff =0.5/sec
Notes:
DNA protein complex’s binding and dissociation is a dynamical process
parameters:
kon =0.021/sec binding rate of dimers to DNA
koff1 =0.04/sec unbinding rate of cI dimer from Or1
koff1 =1.026/sec unbinding rate of cI dimer from Or2
koff1 =5.197/sec unbinding rate of cI dimer from Or3
Note:we get these values from ref(1). In (1) authers estimate these values from experimentally measured protein diffusion coefficient in e.coli and Gibbs free energy.
The replication and degration of plasmid
The plasmid is considered to replicate in a constant rate (r) without the interference of binding protein. Here the parameter reff means the actual replicating rate of plasmid taken the binding protein into consideration.
The transcription of λ cI repressor, notice that λ cI repressor is coded in the plasmid, so the copy number of plasmid will affect the amount of λ cI repressor.
The translation of λ repressor
Plasmid-protein complex affect plasmid replication
If a replication is already initiated but when the replication forks meet a lamda protein on the way, this replication will be aborted. So only when replication forks pass the protein binding point without lamda protein there, the replication processes are effective. This is a simplified model on how plasmid-protein complex affect plasmid replication, we will try to find out some more detailed mechanisms in the future. The probability of a plasmid to become a protein-DNA complex is:
Because of the DNA-protein complex, the effective replication rate of plasmid is
The amount of plasmid protein complex for a set of parameters
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