Team:UNESP Brazil/Model

Model


INTRODUCTION

     The iBioSim program was developed for the modeling, analysis, and design of genetic circuits. We chose this software because it facilitates the visualization of the circuit as a whole since the system is complex and has many connections.

     This project aims to build a biological circuit based on two different fluorescent RNA aptamers, in which their synthesis will be temporally controlled by a system that combines CRISPRa and CRISPRi. Thus, once the circuit is built, it will be activated by the production of gRNAs that will guide the dCas9 fused to the activator protein AsiA in their respective destinations. The temporal control will be done by changing the positioning of dCas9 in the system, through the production of different gRNAs that progress in the reading of the message, allowing the blocking of one promoter and activation of another, generating a time difference in the synthesis of fluorescent aptamers "Broccoli" and "Corn".

     We chose to separate the construction of the system into 3 parts, these being

1) Expression of dCas9 protein regulated by the Ptet promoter;

2) Expression of gRNAS, the first guide RNA of the circuit, regulated by the Pt7 promoter fused to Operon Lac;

3) Reply and message module.

     The first two parts were built having only the control module, and this was done in such a way as to test and optimize the basic parameters, such as ideal concentrations of the activation molecules, IPTG, aTc and Glucose. At each stage of construction, the results were analyzed using graphs and equations provided by the software itself, and adjustments relating to the initial concentrations, degradation rate, leakage and strength of the promoters were analyzed and carried out, and this allowed us to have a better view. clear of the problems we might face in the laboratory during circuit construction, as well as the sensitivity of promoters and molecules in activation.


Back to top


GENERAL MODEL

     We decided to describe our system with deterministic modeling of ordinary differential equations that describe the molecular biology’s central dogma of gene expression inside the cell.


Back to top


REACTIONS

     Here we considered transcription, translation and mRNA and protein degradation rates.

    

    


Back to top


EQUATIONS

     We used the law of mass action to describe the reactants' equilibrium. Here we also considered that DNA concentration doesn’t change with time.

    

    


Back to top


BASIC EQUATIONS

     The iBiosim software uses abstractions, enabling mathematical modeling by a CAD method. Behind the abstraction layer, the software allows the generation of equations that relate all the interactions between the different species present in the model. However, the higher the complexity of the model the greater the resulting system of equations and the complexity of the relationships between them.

     To facilitate the analysis of the available equations, the main equations of the mathematical model describing the circuit biological phenomena are described below. There are 7 main reactions that describe the system regarding to the following processes: (a) and (b) transcription and translation, (c) formation of the complexes, (d) degradation, (e) activation, (f) inhibition, and (g) RNA cleavage.


Back to top


TRANSCRIPTION AND TRANSLATION

    

    


Back to top


COMPLEX FORMATION

    

    

     The complex formation equation describes, for example, the formation of the LacI-IPTG complex, which depends on the kinetics of IPTG-NC formation and is affected by the dissociation (degradation) of the LacI-IPTG complex.


Back to top


DEGRADATION

    

    


Back to top


ACTIVATION AND INHIBITION GUIDED BY THE gRNA

    

    


Back to top


CLEAVAGE OF THE gRNA0-RiboJ-gRNA3 TRANSCRIPT

    

    

     RiboJ is a self-cleaving ribozyme. We assume its activity can be described by a first order equation, i.e. it depends on the concentration of the reagents and the constant kf. The cleavage speed is independent of the activation process, but it determines the speed of the events subsequently displayed by the gRNA attached on it.


Back to top


CONSTRUCTION

     Below we have the complete overview of the construction, with the respective parts highlighted:

    

    

     In the first part, it is possible to analyze the interactions between the tetR repressor protein with the Ptet promoter, which will act by regulating the production of the dCas9 protein fused with the AsiA activator protein.

     We consider the tetR protein to be constitutive, so as long as there is free tetR, it will not be possible to detect sufficient concentration of dCas9 in the medium.

    

    

     In order to obtain temporal control of the tetR protein, a new "species" was added to the model, which in our system corresponds to Anhydrotetracycline, represented as aTc, which will have the function of complexing with the free tetR protein, causing decrease tetR affinity for the promoter. In our model, the temporal control of this reaction was given by the creation of two events, where the Low_aTc refers to the absence and the High_aTc refers to the presence, and these are separated in time so that it is possible to assess the effectiveness of the reaction.

    

    

     The low event is between 0 and 500 time units, with the high event starting from 500.

     The second part, related to the regulation of the production of gRNAS, the system's first guide RNA, can be subdivided into 2 other events: the removal of the repression exerted by LacI using IPTG, and the promotion of production activation through the cAMP-CAP complex.

    

    

     As can be seen in the scheme below, the production of gRNAS is being regulated by the presence of lacI which acts by repressing the promoter and by the presence of the cAMP_CAP complex which acts by activating the promoter. Thus, for the expression of guide RNA to be possible, it is necessary that LacI is removed from the system, which was done with the temporally controlled addition of IPTG, and that there is the formation of the cAMP_CAP complex, which will only occur in the absence of glucose, an event that was also temporally controlled.

    

    

     The presence of IPTG in the medium and the absence of glucose allows the expression of gRNAS, with the increase in the concentration of gRNAS, the formation of the dCas9_gRNAS complex is favored. This biological circuit is based on two distinct fluorescent RNA aptamers, in which their synthesis will be temporally controlled by a system that combines CRISPRa (activation) and CRISPRi (inhibition). Thus, once the circuit is built, it will be activated by the production of guide RNAs that will guide the dCas9 fused to the AsiA activator protein in their respective destinations. Temporal control will be done by changing the positioning of dCas9 in the system, through the production of different guide RNAs that progress in the reading of the message, allowing a physical blockage of one promoter and activation of another, generating a time difference in the synthesis of fluorescent aptamers "Broccoli" and "Corn".

     The dCas9_gRNAS complex induces targt_Sa to produce gRNA0-RiboJ-gRNA3. RiboJ is a ribozyme with autocatalytic activity responsible for the separation of jointly transcribed guide RNAs. After undergoing separation, gRNA0 forms a complex with dCa9, and the complex will activate the production of the broccoli reporter gene and gRNA3 will promote the activation of the next promoter.

    

    

    

     The dCas9_gRNA3 complex induces target_3a to produce gRNA1-RiboJ-gRNA4. The riboJ, again, will separate the co-transcribed guide RNAs. After undergoing separation, gRNA1 forms a complex with dCa9, and the complex will activate the production of the Corn reporter gene and gRNA4 will promote the activation of the next promoter.

     - dCas9 protein production

     In the chart below you can see how the system behaved:

    

    

     Analyzing the graph, it is possible to see that during the low event, that is, in the absence of aTc (represented in red), there is the presence of tetR that grows until reaching equilibrium, as it is a constitutive protein (represented in blue). From moment 500 onwards, when the second event, the high, takes effect, it is possible to notice a peak of aTc that degrades over time. During the period when there is aTc in the medium, the formation of the complex with tetR (represented in yellow) is clear, as well as the presence of dCas9, which is enough to conclude that the model is working satisfactorily.

     - gRNAS production

     In this part of the model, the main point evaluated was whether the gRNA production was really being dependent on both events, as this would make the construction safer and more robust. In the chart below it is possible to analyze the results obtained:

    

    

     At first, up to time 1250, it is possible to see the presence of free LacI in the system, which is due to the absence of IPTG, and the presence of the cAMP_CAP complex, which is due to the absence of glucose. From 1250 onwards, when the IPTG event starts, there is a drop in the concentration of LacI, which can be interpreted as a good indication that the system is responding as expected, in addition, the formation of the complex between LacI and IPTG. In blue we can see the formation of gRNAS, due to the presence of IPTG and the absence of glucose, which is another indication that the system is acting as expected. At 1750 the glucose event started, which as expected promoted a drop in the cAMP_CAP complex, and consequently a drop in gRNAS. The overlapping of events that occurs between 1750 and 2000 gives us the assurance that the two requirements, the absence of glucose and the presence of IPTG, are being necessary for the production of gRNA, and that there are no leaks, therefore the system is being very well controlled temporally.

     - gRNA0 and gRNA3 production

    

     The formation of the LacI_IPTG complex removes LacI from the medium, thus enabling the gRNAS, in light blue, to be formed. From time 1250s on, targt_Sa produces gRNA0-riboJ-gRNA3. The guides appear in the graph separately (gRNA3 in red) and (gRNA0 in dark blue) due to the cleavage action of RiboJ.

     Once the gRNAS, in blue, is formed, the other guides appear in the graph (gRNA3 in red) and (gRNA0 in lilac).

     After undergoing a separation, gRNA0 forms a complex with dCa9, and the complex will activate the production of the broccoli reporter gene (in blue), and gRNA3 will promote the activation of the next promoter.

     The dCas9_gRNA3 complex induces target_3a to produce gRNA1-RiboJ-gRNA4. The riboJ, again, will separate the co-transcribed guide RNAs.

     After undergoing a separation, gRNA1 forms a complex with dCa9, and the complex will activate the production of the Corn reporter gene (in red).

     The circuit aims to create a time difference in the synthesis of the fluorescent aptamers so that we can see the peaks of Corn and Broccoli separately, however, when the construction was ready, the peaks of the two aptamers were overlapping.

     So, we decided to change some constants, strength of promoters, rate of degradation of gRNAs, but nothing brought satisfactory results. Only with the change in the rate of formation of the gRNA0 and gRNA1 complex we obtained the results of figure 11.


Back to top


PARAMETERS ESTIMATION AND ASSUMPTIONS

     We don’t always find the exact parameter value that we are need. Sometimes we have different sources providing completely different values for the same thing. That’s why sometimes it’s necessary to make assumptions and estimations in order to reach the most realistic results.

    Click Here to Download the Parameters Table!


Back to top