1) Established a general idea of how our system works (Metal Aptamer sensor and Leptospirosis detector).
2) Constructed useful reaction schemes to represent how our system works.
3) Derived differential equations from reaction scheme using mathematical laws.
4) Estimated reaction constants by reading through related literature and using acquired information to make reasonable estimations.
5) Implemented differential equations with related reaction constants into MATLAB as functions.
6) Produced graphical representations showing fluctuations in molecule number of each species.
7) Devised potential experiments that could be conducted to characterise/parameterise model more accurately.
Team:Warwick/Model
Summary
Introduction
The Warwick iGEM team decided to use a CRISPR/Cas9 system to build a sensing device for Leptospirosis detection. CRISPR technology is a relatively new, not fully understood technology, so for our project to be successful, it was imperative that we have as detailed an understanding of the way the technology operates as possible. As a result, we spent a lot of time trying to develop a model that accurately represents the behaviour of our system.
How the system works/What parts we decided to model?
For us to be able to model our system, we had to establish what we thought would be happening while our device was in action. Before our system could start sensing Leptospirosis RNA, we had to produce the three plasmids that in turn produced the sensing complex. Once these plasmids had been constructed, the sensing process could begin.
At the start of the sensing process, when our system is in any environment, Plasmid 1 produces the dCas9. Plasmid 1 is also capable of making GFP. Plasmid 2 produces the RNA binding protein with the attached Effector while Plasmid 3 makes the sgRNA. All of these products are released into the surrounding environment in large quantities.
Our sgRNA design incorporates a region that is complementary to dCas9 molecules that we call the dCas9 handle. When the sgRNA is in its original shape, the handle is not accessible to the dCAs9, however, if there is Leptospirosis RNA present in the environment, it will bind to the sgRNA, changing its shape and allowing the dCAs9 to bind to it.
The dCas9/sgRNA complex is guided back to Plasmid 1 by the dCas9 component. When the dCas9/sgRNA complex is bound to Plasmid 1, the dCas9 molecule then acts as a beacon for the RNA binding protein with the attached effector to find the sgRNA and bind to it.
When the previous binding process is complete, the RNA binding protein/effector recruits an RNA polymerase, allowing it to read the gene for GFP production present on Plasmid 1. GFP is produced and is released into the surrounding environment.
When establishing the way that our system operates, we made the following assumptions to make the modelling process easier:
1) Each step of the process happens one step at the time (so two species binding simultaneously does not happen).
2) The RNA being sensed has a strong binding affinity to our sgRNA and will not unbind once bound.
3) The sgRNA will be produced in relative abundance relative to the other species in the environment.
After having established the way we expected our system to perform, we decided that it would be most useful to model the rate of change of concentration for the different molecules that would be present in our system at any given time.
Our ultimate goal was to accurately predict the amount of GFP being produced. This would give us an insight into how sensitive our detection device will be with differing amounts of Leptospirosis RNA present in a system.
Method
In order to start modelling our system, we needed to construct a reaction scheme to apply modelling techniques to. The aim of applying these modelling techniques to our reaction was to derive ordinary differential equations that would dynamically represent the behaviour of our system over a given period of time. We will now explain the process that we went through to refine our reaction scheme, in the hope that future iGEM teams may learn from our mistakes or improve on our model.
Initially, we constructed a reaction scheme that showed step by step what would happen when our system is detecting Leptospirosis, in the case where the Leptospirosis RNA is present. This reaction scheme is shown below:
1) T0→mRNA→ dCas9
2) T0→ mRNA→ RNABP + Eff
3) T0→sgRNA→ sgRNA + Leptospirosis RNA
4) sgRNA + dCas9 + RNABP/Eff ↔ dCas9*
5) dCas9* + Plasmid 1 → Plasmid 1*
6) RNABP/Effector + RNA Polymerase ↔ Active RNA Polymerase
7) Active RNA Polymerase → GFP
ODEs from this reaction scheme:
Model for GFP Production:
Key: T0 = Starting time, dCas9 = deactivated Cas9, RNABP = RNA Binding Protein, Eff = Effector, GFP = Green fluorescent Protein, KA = Association constant, h = Hill coefficient, A = Active RNA Polymerase
The ODEs were derived by applying the law of mass action to the reaction scheme. To model the production of GFP, we used a Hill activation function. These modelling techniques are explained in more detail later on.
We came to realise that the reaction scheme above is not an accurate representation of what could actually happen in our system. It only showed what would happen with our system in the ideal case, being that everything formed at the right time and in the right order with Leptospirosis RNA present in the system. It was possible for our full activation complex to be formed in different orders.
For example, it was possible for our sgRNA to bind to the plasmid before or after it had bound the RNA binding protein. This is significant because the association/dissociation constants for the different potential formation processes mean that the concentrations of the different species may be slightly different.
So we then decided to construct another reaction scheme that showed in greater detail what was going on when our system detects Leptospirosis. This reaction scheme assumed that only one process could happen at a time.
General ODEs derived from this reaction scheme:
We felt that the second reaction scheme was a lot more accurate with regards to representing our system. Another advantage of using this reaction scheme is that it showed the reversibility in all of the steps. However, it immediately became apparent that this reaction scheme may cause confusion.
