Team:UANL Mty-Mexico/Modelling/Biphasic Switch

One of the main elements of our project is the “Biphasic Switch”, as dubbed by Chris A Voigt in his review Genetic Parts to Program a Bacteria (2006).

As any other switch, the Biphasic Switch can turn the system from one state into another according to the input signals, which usually are of different kinds, e.g., two different chemical inductors. Nevertheless, our Biphasic Switch can change between two states in response to the concentration or intensity of only one kind of input signal. This input signal could be of chemical (e.g., IPTG or Arabinose) or physical nature (e.g., light).

The behavior of the Biphasic Switch relies on the ability of the Lambda phage cI protein to function both as an activator and as an inhibitor at the pRM promoter, Court, DL, et al., (2007). The pRM promoter is composed of three operator sites: O1, O2 and O3, to which cI binds cooperatively with different affinities. Briefly, when cI is at certain concentration, it binds to the O1 region and facilitates the cI binding to operator O2. In this conformation, the pRM promoter is activated. But as the cI concentration rises, it reaches the affinity threshold towards operator O3 and gets attached to it, repressing the pRM activity.

In our model, we include the affinity change due to the cooperativity effect and the dual behavior of cI. The affinity shift towards O2 and O3 is regulated by a logic rule regarding cI concentration, so when cI concentration is below its dissociation constant towards O1, the dissociation constant towards O2 and O3 remains at basal levels. But when cI concentration rises above its O1 dissociation constant, the cooperativity effect takes place and the dissociation constants towards O2 and O3 are lowered, increasing cI affinity.

Finally, we modeled the dual behavior of cI by considering operators O2 and O3 as if they were different promoters. Thus, their effect on the change of the regulated gene’s concentration is reflected in two different elements of the differential equations, one for activation at O2 and another for repression at O3. The different dissociation constants towards O1, O2 and O3, both for basal activity and for the cooperativity effect, were calculated from the total free energies for the binding of cI to the three operators published in Ackers, GK, et al., (1982) and according to the formula presented there. The effect of cI on its regulated genes is then represented as follows:

IMAGEN:cI effect on its regulated genes.png

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.