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Lysis Cassette

Sam7 Mutation

RPU (Relative Promoter Unit)

Though BioBrickTM parts are standardized in terms of how individual parts are physically assembled into multi-component systems, many of them are not standardized in the point of characterization. 
Unfortunately, it is known that the absolute activity of BioBrick promoters varies across experimental conditions and measurement instruments [1]. However, Kelly et al found that this variation could be reduced by measuring the activity of promoters relative to BBa_J23101 which is a promoter as an in vivo reference standard for promoter activity by ~50%. They defined a Relative Promoter Units (RPU) in order to report promoter characterization data in compatible units. In order to measure RPUs of promoters, the synthesis rate of Green Fluorescent Protein (GFP) encoded by mRNA transcribed from each promoter is observed.
RPU is defined by Equation 1:
   Relative activity of promoter φ (RPUs)=〖PoPS^SS〗_φ/〖PoPS^SS〗_J23101 
PoPS (Polymerase Per Second) is the unit of absolute “promoter activity”, and “promoter activity” is defined  as the number of RNA polymerase molecules that pass by the final base pair of the promoter and continue along DNA as an elongation complex. PoPSSS is PoPS at the steady state of following system(d[M]/dt=0, d[I]/dt=0, d[G]/dt=0:
 (d[M])/dt=n*PoPS-γ_M [M]
(d[G])/dt=a[I]-γ_G [G]

[M] is the concentration of mRNA, [I] is the concentration of immature GFP, [G] is the concentration of mature GFP,

γ_M is the mRNA degradation rate,
a is the GFP maturation rate,
γ_I is the degradation rate of immature GFP
n is the copy number of the plasmid containing the promoter

ρ is the rate of synthesis of immature GFP in absolute units of protein per second per mRNA. By combining equation 2, 3, 4 and 5 at the steady state, equation 6 and 7 are obtained: 〖 S〗_cell=a[I]


Here Scell is define as the per cell mature GFP synthesis term.

  PoPS^SS=(γ_M (a+γ_I)〖S_cell〗^SS)/ρan
 PoPS^SS=(γ_M (a+γ_I)〖γ_G G_cell〗^SS)/ρan

Here Gcell is define as the per cell mature GFP synthesis term. From equation1 and 6 RPU is described as equation8.

RPU= ((γ_(M,φ) (a_φ+γ_(I,φ) ) 〖S_(cell,φ)〗^SS)/(ρ_φ a_φ n_φ ))/((γ_(M,J23101) (a_J23101+γ_(I,J23101) ) 〖S_(cell,J23101)〗^SS)/(ρ_J23101 a_J23101 n_J23101 ))
If the test promoter φ and the reference standard promoter are measured under the same culture conditions and both promoters are carried on the same backbone plasmid, following equations are approved.

a_φ=a_J23101=a (10) n_φ=n_J23101=n (11) γ_(M,φ)=γ_(M,J23101)=γ_M (12) ρ_φ=ρ_J23101=ρ (13)

 From equation 9, 10, 11, 12 and 13, Equation 14 is accomplished.

RPU= ((a+γ_(I,φ) ) 〖S_(cell,φ)〗^SS)/((a+γ_(I,J23101) ) 〖S_(cell,J23101)〗^SS )

 In addition, immature GFP is stable so that protein degradation is negligible compared to dilution due to cell growth (γI,φ=μφ and γI,J23101=μJ23101, where μis the cellular growth rate). Therefore, equation 14 can be modified to equation 15:

RPU= ((a+μ_φ ) 〖S_(cell,φ)〗^SS)/((a+μ_J23101 ) 〖S_(cell,J23101)〗^SS )

And if the growth rates of both strains are almost same, equation 16 is approved.

if |μ_φ-μ_J23101 |≪a ,((a+μ_φ))/((a+μ_J23101))≈1

Accordingly, we can make equation 17 from eqution16.

RPU= 〖S_(cell,φ)〗^SS/〖S_(cell,J23101)〗^SS


ScellSS can be described by equation18: 〖S_cell〗^SS=(dF/dt)/ABS


Therefore, RPU is described by equation 19: RPU= ((dF_φ/dt)/ABS_φ)/(〖(dF〗_J23101/dt)/ABS_J23101 )


We can also establish equation20 from equation1, 6, 10, 11, 12 and 13. RPU= 〖[G]〗_(cell,φ)/〖[G]〗_(cell,J23101) *μ_φ/μ_J23101


RPU can be calculated from equation19 or equation20. Therefore, we have to observe GFP synthesis rate and ABS (OD600) of both strains or to measure GFP concentration per cell and growth rate of both strains to measure RPU. To see how to measure RPU practically, go protocol. To see more about RPU, go reference.

Reference 1. Jason R Kelly et al. ”Measuring the activity of BioBrick promoters using an in vivo reference standard.” Journal of Biological Engineering 2009, 3:4