Team:UANL Mty-Mexico/Modelling/Biphasic Switch

Where α is the maximum transcription rate; [cI] is the cI protein concentration; O2Kd is the dissociation constant of cI towards the O2 operator; O3Kd is the dissociation constant of cI towards operator O3; and µ is the degradation rate of the mRNA. Note that both the cI protein concentration and the dissociation constants have an exponent. This exponent is the Hill coefficient and equals two.

The figure 1 is a diagram of a Biphasic Circuit that responds to an IPTG input. The LacI gene is obviated.

IMAGEN:Fig 1 Diagrama

In brief, after the addition of IPTG to the culture, the LacI repression begins to cease, allowing cI to be expressed. This rise of cI concentration is supposed to be dependent on the IPTG input concentration, so that at low IPTG, the induction of cI is expected to be also low and in the range of the pRM activation state. On the other hand, when the IPTG input is high enough, the high cI induction will switch pRM into its repressed state.

The pRM is controlling the expression of two genes: the reporter GFP and another transcription factor cI434, which is negatively regulating the expression of another reporter gene, YFP. This reporter gene is also regulated by cI, but in a positive manner at any concentration considered. In this way, when the pRM promoter is active, GFP and cI434 will be expressed, giving rise to the first state of our Biphasic Switch, i. e., the green state. Conversely, when pRM is inhibited by the high concentration of cI, the inhibiton by cI434 will be gradually released and the second state will be observed, i. e., the yellow state (because of YFP).

Imagen: Fig 2 Simulacion uno

The time for the IPTG addition in all simulations is at 300 min. We considered a simulation time of 1000 min just for the sake of clarity in the graphs, but the actual experimental times may be shorter. In all the graphs shown, the Y-axis represents protein concentration in nM units and the X-axis represents time in minutes.

The initial condition of the LacI concentration was determined in a simulation where, without any disturbance, the LacI gene was let to reach its saturation level. This saturation level is taken as an initial condition in order to avoid noisy behavior at the first minutes of simulation. Furthermore, in the wet-experiments, these simulated initial conditions may represent the incubation time previous the IPTG input, when the cells are allowed to grow, express LacI without disturbance and sustain the repression of the cI gene and of the Biphasic Switch as well. As seen, the green state is almost undetectable throughout the whole experiment, while the yellow one is activated with cI activation.

For cI to act as expected, i.e. a dual effect transcription factor, there must be some changes to the original circuitry, starting with modifications in LVA tags (all genes are considered to have one), RBS activity differences and perhaps some connectivity modifications.

The simulations in Figure 2 were performed considering that all genes have the same RBS efficiency. But in order to simulate the effect of different RBS, we assumed that protein translation is proportional to the activity of the specific RBS present in its mRNA. We decided to use the RBS Community Collection from the Registry of Standard Biological Parts (http://partsregistry.org/Ribosome_Binding_Sites/Prokaryotic/Constitutive/Community_Collection) because this set’s relative efficiencies have already been characterized.

We are aware that multiplying the maximum transcription rate times the relative RBS efficiency gives only a relative result, because the RBS characterization doesn’t report efficiencies in a nM concentration scale. The best approach would be to determine the ratio between the theoretical maximum translation rate and the translation rate for a given RBS, all in nM units. For this reason, the simulations of the RBS effects are reported in relative units, assuming that maximum transcription rate is achieved with RBS BBa_B0034, i.e. the reference RBS of the Community Collection. The RBS Relative Units are proposed as a unit measure for gene expression in our simulations, as the actual behavior of the protein concentration dynamics in nanomolar units can be also reflected in relative units, considering the basal signal as zero.

We decided to modify the RBS from cI, GFP and YFP. Protein cI was selected in order to maintain its concentration in a low range for some time, so that GFP inhibition can be delayed. Protein GFP was selected in order to increase its translation rate when using the most powerful RBS of the set. And finally, protein YFP was selected in order the noise it generates when the green state is turned on. Also, LacI LVA tag was removed, increasing its half-life. Furthermore, two LacI genes are considered in simulation D. The relative strengths of the RBS for the genes are the following: