E = the expression of one of the fluorescent protiens (RFP) when there is transcription of the CFP RNA at any particular level as a proportion of the expression of RFP at the same transcription rate when none of the CFP RNA is present within the cell. So if the promoter (PYEAR) attached to the rfp and construct 1 was expressing at a constant rate with promoter 2 entirely switched off then promoter 2 started transcribing and the amount of rfp in the cell halved then the value of EA would be 0.5 at that transcription rate of CFP (0-1)
E = the expression of one of the fluorescent protiens (RFP) when there is transcription of the CFP RNA at any particular level as a proportion of the expression of RFP at the same transcription rate when none of the CFP RNA is present within the cell. So if the promoter (PYEAR) attached to the rfp and construct 1 was expressing at a constant rate with promoter 2 entirely switched off then promoter 2 started transcribing and the amount of rfp in the cell halved then the value of EA would be 0.5 at that transcription rate of CFP (0-1)
E = the expression of one of the fluorescent protiens (RFP) when there is transcription of the CFP RNA at any particular level as a proportion of the expression of RFP at the same transcription rate when none of the CFP RNA is present within the cell. So if the promoter (PYEAR) attached to the rfp and construct 1 was expressing at a constant rate with promoter 2 entirely switched off then promoter 2 started transcribing and the amount of rfp in the cell halved then the value of EA would be 0.5 at that transcription rate of CFP (0-1)
L = the length of the DNA strand that is transcribed (Leader and protein coding region) .
C = the rate of transcription
L/C = the period of time taken for transcription to take place, the time in which translation can be initiated but it is unlikely that the two leaders will bind to one another
A = the rate of transcription of promoter 1 (the PYEAR) as a proportion of it’s maximum possible transcription rate (0-1)
A*(L/C) = the number of RFP RNAs that can be translated independently of the presence of other RNA at any one time and so is proportional to translation (and expression) from DNA ascociated RNA (RNA that is still being transcribed). This occurs both when the CFP RNA is and isn’t present so has to be on both the top and bottom of the equation.
H = Half life of the RNA after transcription
L/C + H = the full time for which the RNA would be translated assuming no interactions between leaders for instance when only one of the promoters is inducing transcription.
B = the transcription of the second promoter within the cell as a proportion of the maximum possible transcription of that promoter (0-1)
Because there can not be negative expression of A (only positive expression of B to represent negative expression of A) the translation of the RFP RNA(A) = A - AB .
It also has to be remembered that there will never be full interaction between the two RNA leaders, particularly at low concentrations if only because the two strands never come in to proximity or because of cellular processes; consequently the function B/(D+B) must be used giving the formula; translation of the RFP RNA(A) = A – A (B/(D+B))
D is a constant of the biological system whose derivation is so complex that it can only really be calculated through observation but can be modelled at various levels.
So to bring it all together; the top half of the equation indicates the degree of translation of the RNA transcribed by the first promoter under any particular transcription rate of the two promoters in arbitrary units. To make this into a meaningful output it is divided by the maximum translation rate at that rate of transcription to equal EA ; this indicates the degree of attenuation of one RNA from the other.
To get the degree of translation of the other RNA (EB) just swap A for B throughout the equation.
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