Difference between revisions of "Team:Thessaloniki/Model/dCas9"

After the study of TALE system we moved on to the study of the model, which uses as repressor the complex dcas9-sgRNA, whose schematic representation is shown in Figure 1.

This system, consists of three subsystems.The main subsystem, is the one that replaces the system of TALE and has the same functionality. The only difference is that now the repressor consists of the complex dcas9-sgRNA and for that reason, instead of the transcription and translation of the repressor, we just have a binding of the two molecules. The other two subsystems which were studied are about the creation of those two molecules. The dcas subsystem works with extra repression for its production, which is controlled via Doxycycline.In contrast, the sgRNA subsystem operates by activation through Rhamnose-RhaS complex which is also adjustable.

For each one of those subsystems, we have studied separately their characteristics and the parameters which affects more the output of every subsystem. In order to achieve that, we used the knowledge that we gained from studying the TALE system. Along the way, we realized possible problems and gave solutions to them, which we then shared with Wet lab, so as to integrate them in system design.

We started by studying the dcas subsystem. The dcas is repressed by the tetR, because in large quantities can be toxic for the cell. Also, by adding doses of Doxycycline, which in turn creates complex with tetR, we managed to decrease the repression that happens in dcas to the desired level.

As shown in Figure 1, the dcas9 and the tetR are on a different plasmid than the rest of the system. This means, that the change in copy number that we examine does not affect the plasmids which are responsible for the production of the dcas9 and the tetR. After the completion of the modeling process, an analysis was held to consider other options that Wet lab proposed, regarding the different expression sites of dcas.

For the mathematical representation of the system, we took into consideration the following assumptions:

• Inducer dynamic Doxycycline: We assume that as soon as Doxycycline is injected into the solution, is stabilised in a steady state inside the cell and we do not take into account influx and outflux rates.The concentration of Dox inside the cell is set to 8ng/ml, that is 2.4 mM. When the complex [TetR: Dox] is degraded with the same rate as tetR, we assume that Dox can be free inside the cell again.
• tetR dimerization, binding to Doxycycline and binding rate to tetO2 operator sites: A tetR dimer is sufficient for specific binding to the operator sequence. However, a tetR monomer is unable to bind and exert any repressive effect. Thus, we assume that the repressor dimer binds to the operator (denoted as species O) with a one-to-one stoichiometry and also assume that a dimer binds one to one with Doxycycline. These assumptions are valid, as monomers forming a dimer and dimer forming a complex with Doxycycline are very fast interactions and do not affect other simulation components. As a consequence, we halved the translation rate of tetR and the concentration of Doxycycline that was injected into the solution.
• We expressed the Hill equation as mass action kinetics for the two different states as we did in TALE system.

The subsystem is described by the following chemical reactions and differential equations, which we used to implement the simulation in Simbiology, and also in python.

Parameter estimation

For parameter values, first estimates were made through bibliography and methods which were used also for TALE, such as RBS Calculator.

The parameters for which it was deemed necessary to do further analysis, as bibliographic references proved to be quite uncertain, are the binding and unbinding rates between doxycycline and tetR and also those of tetR with DNA, in the two position of pTet promoter. So the sensitivity analysis, was applied to these parameters.

As can be seen in Figure 2, the kon2 between tetR and DNA shows approximately 0.6 first order index and taking into account also higher order interactions, this is the most influential parameter of the system. The toxicity of dcas is an important limiting factor which we should consider.Therefore, its concentration must be under control via the tetR repression and the Doxycycline dose.

Taking into consideration all the above, we decided to examine the system behaviour with different sets of parameters. Specifically, we used all the parameters that was used in sensitivity analysis and we created 5000 different sets. The values of the kinetics ranged from 0.001 to 10.

The data from the analysis (Figure 3), indicate that the mean value of dcas9 concentration is approximately 0.826 nM. This result appears to be problematic, as a concentration this low, would set an upper bound on the final repressor and by extension, sfGFP could not be independent from the copy number, in any case.

While trying to locate the problem, we noticed that, in order for the system to acquire a reasonable dcas concentration, we had to change its dissociation constant, .In Figure 3, kd’s maximum value is ,but scanning this parameter for a bigger range we found that if we increase it to ,we will finally get satisfying results.

After we shared this result with Wet lab, combined with the fact that the kd for which our system works, disagrees with those found in bibliography [4][5], we decided to make an experiment to validate the functionality of the dcas subsystem. [ ΠΛΗΡΟΦΟΡΙΕΣ ]. The results of the experiment, indicate that dcas is produced, in very good level, without causing any problem for the cell growth.

The reason that the concentration of dcas in the model depends that much by tetR’s ability to bind to DNA, we believe is due either to wrong configuration of tetR or to the modeling of the Doxycycline dose in the system. Having received the feedback from the experiment, we wanted to correct the model so as to bring the right result. We decided, to not change the modeling of the dose, but to adjust the concentration of dcas, by changing the aforementioned kd as seen in Fig.4. We ended up, that the value of the constant must be equal with as its concentration is greatly increased for other, bibliography based, values [2].

The sgRNA is produced by the promoter Pbad, only when he is activated by the complex Rhamnose-RhaS. In contrast, with the repressed function of dcas, the sgRNA is activated by that complex and that is induced by Rhamnose, which we add as a dose to the system.

As shown in Fig.1, the production of protein RhaS is done by the genome of the cell and therefore the concentration is independent from changes in its copy number of sfGFP. From that fact, we can understand that the complex which it creates with Rhamnose has this upper limit in each experiment for different copy number. The exact amount of complex and by extension the activation for the production of sgRNA, will directly depend from the Rhamnose that will be provided to the system.

For the mathematical representation of the system, considered the following assumptions:

• Inducer dynamic Rhamnose: Stabilization of Rhamnose as soon as it’s injected to the solution. As Rhamnose degradation rate is quite lower than this of rhaS, we assume that the degradation rate of the complex is the same as rhaS degrade. When rhaS degrades the free Rhamnose molecule is added to total Rhamnose concentration.
• RhaS dimer and binding rate to operator site of PrhaBAD:Like in tetR, we assume that Rhas is produced as a dimer because of it’s fast dimer binding. Because of its fast binding with L-Rhamnose we also assume, one to one stoichiometry. In the presence of L-rhamnose, its concentration is 0.02 g/ml or 1.2 mM, Expression from the rhaBAD promoter is log linear with n=1 [7] with respect to inducer concentration.
• Again, Hill equation was expressed as mass action kinetics equations.

The following chemical reactions and differential equations were used to describe the system mathematically:

Parameter estimation

After using a bibliographic approach (see bibliography based estimation) to find the parameter values of the subsystem sgRNA, we ended up in the following uncertain parameters:

• Binding and unbinding rates of Rhamnose with RhaS.
• Binding and unbinding rates of Rhamnose:RhaS complex with Pbad promoter.
• Degradation rate of RhaS

We applied sensitivity analysis for these parameters, using the same rate ranges as dcas9 subsystem and the degradation variation is 0.001 to 1. The results are shown in Figure 5 where you can see that the most influential parameter is clearly the binding rate to Pbad promoter.

Binding and unbinding rates of RhaS to Rhamnose do not have any effect at all and we assume this is due to the very big concentration of Rhamnose in the system. (set to 1.2 mM) Τhe other two parameters have relatively high total order indices because of their interaction with kon (same differential equation).

In order to get more insights regarding the system behaviour, we applied a robustness analysis, shown in Figure 6. The result appeared as expected with sgRNA concentration increasing for higher copy number. The standard deviations show us that for little copy number the variation of the concentration is trivial but for higher copy numbers the variation increases accordingly. However, we can clearly tell that for most parameter sets the linearity of the system cannot be ruined.

The main system consists of the formation of the repressor complex and the production of sfGFP, which is being repressed by the complex. The complex binds to DNA slowly, as dcas9 has to find the PAM sequence.The dissociation is also very slow and approaches the dillution rate of the cell. The disruption percentage of RNAP, arises from sgRNA’s complementarity with DNA and the concentration of polymerase. We also assumed the degradation of the repressor complex, being the same rate as dcas9 degradation.

Parameter estimation

As previously done with the subsystems we studied bibliography to find out about system parameters and their ranges. After that, we applied sensitivity analysis for the association and dissociation constants. Interestingly, the results showed that the repressor’s kdson and kdsoff does not affect the system output. After changing some values of these parameters we found that this is true and the system appeared to be very robust regarding the repressor concentration. Due to the strong repression that it does, combined with its very small degradation rate, the repressor is binding to DNA and almost never dissociates, thus making small repression concentrations sufficient for the system to work. Specifically, using different values we were able to get exactly the same output error with many combinations of kdson and kdsoff.