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Suppose a simple synthetic construct, consisting of a constitutive promoter and a single gene: construct

One of the simplest ways to model GFP transcription is to use an ODE:

$\frac{d [GFP_{mRNA}]}{dt} = a - b{\cdot}[GFP_{mRNA}]$

where $a$ is GFP transcription rate and $b$ is GFP mRNA degradation rate (both constants). Normally, we assume $a>>b$.

Suppose we wish to account for plasmid concentration with the value of transcription rate $a$ - e.g. with higher plasmid concentration, the ratio $a/b$ should increase as the mRNA saturation levels are expected to be reached faster. In other words, suppose we transfect 2 individual constructs depicted above, 10 ng of one and 30 ng of the other - how should this difference in concentration impact the rate constants values, assuming the constructs are otherwise identical?

Assuming this, approximately how does gene transcription rate $a$ change as a function of the amount of transfected plasmid containing the above construct? Ideally, I'd be interested in knowing this for HEK 293 cells, but any other decent estimation is acceptable. One simple option is to simply assume linear relation, but I think that's too simplistic: e.g. if we say $a=1$ at 10 ng plasmid concentration, then $a=3$ at 30 ng plasmid concentration. Note that I'm not necessarily limiting myself to ODE models, just looking for some kind of relation.

I have so far not been able to find anything useful in papers I've examined, so any help would be appreciated.

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The amount of transfected plasmid does not correlate at all with the protein expression level. After transfction, usually each cell is going to get and keep only one copy of the plasmid. Once the plasmid is in the cell, it will be replicated and the cell will contain X copies of it, depending on the plasmid copy number. In general, plasmids with low copy numbers correlate with lower protein expression compared to plasmids with high copy number. But there are also exceptions:

Expression of genes under control of EF1α promoter appears to correlate with plasmid copy number. In contrast, expression driven by the more traditional CMV immediate early promoter appears less plasmid copy number dose-responsive (ref).

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Well.. the copy number does matter in case of CMV also. I had observed normalized luciferase activity in HEK cells at different amounts of transfected plasmid- it shows difference. Also, the effect on an miRNA on the luciferase is better as the concentrations decrease. It is not strictly linear, though. –  WYSIWYG Mar 5 at 6:14
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