Difference between revisions of "Team:OUC-China/Model"

The endoribonuclease Csy4 from CRISPR family is the main role of the miniToe system. Csy4 (Cas6f) is a 21.4 kDa protein which can recognize and cleave a specific 22nt RNA hairpin which consists of an N-terminal ferredoxin-like domain and a C-terminal domain. The later domain constitutes most of the recognition interactions with the RNA. The RNA adopts a stem-loop structure (the specific 22nt RNA hairpin) with five base pairs in A-form helical stem capped by GUAUA loop containing a sheared G11-A15 base pair and a bulged nucleotide U14. In the binding structure of Csy4-RNA complex, the RNA stem-loop straddles the β-hairpin formed by strands β6-7 of Csy4. The Fig.1 and Fig.2 shows two structure of Csy4: with and without the hairpin bound.

Based on the function of Csy4, we designed a new cis-regulatory RNA element named miniToe, which can be recognized by Csy4. The whole system works as a translational activator including three modular parts:

1. A cis-repressive RNA (crRNA) serves as a translation suppressor by pairing with RBS, and therefore constitutes the critical part of the miniToe structure.
2. A Csy4 site serves as a linker between cis-repressive RNA and RBS, which can be specifically cleaved by Csy4 enzyme.
3. Csy4 enzyme --- A CRISPR endoribonuclease.


Fig.4 and Fig.5 blow show the two complex of miniToe structures: with and without specific site of hairpin cleaved, which is called the precursor complex and product complex respectively.

All the reaction happened in our miniToe system can be described chronologically by following five main steps in Fig.6:

(1) The miniToe is produced and accumulated.
(2) Csy4 is produced after induced by IPTG.
(3) Csy4 binds to the miniToe structure and forms the Csy4-miniToe complex.
(4) Csy4 cleaves the special site and divides the miniToe structure into two parts: the Csy4-crRNA complex and the mRNA of sfGFP.
(5) sfGFP is produced.

From the description above, we can get four key problems in our system to make sure whether our system can work successfully:

(1) Can Csy4 dock correctly with the miniToe structure (hairpin)?
(2) How about the ability of binding between the Csy4 and miniToe structure (hairpin)?
(3) How about the ability of cleavage between the Csy4 and miniToe structure (hairpin)?
(4) Can cis-repressive RNA be released from the RBS successfully?

According to the work process, we built an ODEs model and simulated our miniToe system for 30h, the result can be seen in the Fig.7.

We compared the experimental data to the simulation result, find it fit perfectly as Fig.7 shows.
  To see more details

The main work our molecular dynamics is to give an explanation for the experimental data at atom level and the four key points we have discussed before. The experiment has proved that miniToe is working well, which means the four key points work well too. We will present you the result of molecular dynamics following the four key points.

For the first key point, we have the interaction matrix to describe the molecular docking, and the heatmap of the matrix can be seen in Fig.9.


For the second key point, we calculated the binding free Energy of Csy4/RNA complex. The result of binding free energy for wild-type Csy4 is $△G_{binding}=-59154.9251\stackrel{}{}kj/\text{mol}$ .

For the third key point, we checked the distance of Ser151(OG)-G20(N2’), which is a key interaction in the active site of Csy4 to describe the ability of cleavage. The distance curve of Ser151(OG)-G20(N2’) for wild-type Csy4 can be seem in Fig.10.




For the last key point, we used the RMSD of product to describe the release of crRNA. The result can be seen in the Fig.11.
The RMSD is unstable and give an explain to experiment that crRNA is release from RBS.

  To see more details

When we made the sensitivity analysis for our ODEs model, we found that the cleavage rate of Csy4 can influence the expression in GFP, which indicated that once we changed the wild-type Csy4 into some mutation, we can achieve the different expression of GFP. The Fig.12 shows what will happen in the GFP expression curve if we change the cleavage rate of Csy4. It can achieve the goal of different level of regulation.

We found four important sites in wet lab, Gln104, Tyr176, Phe155 and His29, which play important roles in binding and cleavage in Csy4 structure.(Fig.13) Considering the existing 20 amino acids in nature, there were 80 mutants to be explored if we had only one site to be mutated.


In Q3, we have discussed four key points which can directly influence our miniToe system. In addition, according to the molecular dynamics results in Q5, we can describe the four key points through four significant symbols.

Now we are going to construct a logic line to show how to use the three main information above to design Csy4 mutants:

What we have proved through the experiment is that the wild-type Csy4 can work well with the miniToe system, which means that all the key points we have discussed before didn't affect the wild-type Csy4. The wild-type Csy4 can dock correctly with the miniToe structure and had a good ability to bind and cleave the miniToe structure. Finally, the crRNA can be released from the RBS. So we choose the wild-type Csy4 as a standard, and all Csy4 mutants can check the four points by comparing with wild-type Csy4.

Now for the four points in Q3 we have discussed the mathematical forms in Q5. And the most important thing is how to make a comparison between the mutant and wild-type Csy4 enzymes, which will be discussed in Q8.

In Q7, we have discussed the full logic lines about how to design the Csy4 mutants. Here we will give the comparison method for the four key points in miniToe system. And we did this comparison between the mutant and wild-type Csy4 enzymes.

Now we have four mathematical forms including two curves, a numerical value and a matrix. Four things can be divided into two kinds of data: the matrix and the numerical value. The interaction matrix and the curve can be regarded as a matrix because the curve is discrete, and the binding free energy is a numerical value.

We used Euclidean distance to describe the difference between the two matric:


We used the formula below to calculate the difference of binding free energy between the wild type and mutants:



According to description above, we defined four value to compare the four key points between the mutant and wild-type Cys4 enzymes: $D_1(\mathrm{int}teraction\stackrel{}{}matrix)$ , $\ln (K_{drel})$ , $D_3(Ser151-G20\stackrel{}{}curve)$ , $D_4(RMSD)$ .

By using the four values, five Csy4 mutants were designed and shown in table below.

Csy4	$D_1$	$\ln (K_{drel})$	$D_3$	$D_4$
WT	0	0	0	0
Q104A	0.483	2483	9.48	30.82
Y176F	0.592	-382	11.61	40.62
F155A	0.233	-1627	13.41	35.71
H29A	0.173	833	15.29	316.22

The design of hairpin mutants is quite different from the Csy4 mutants due to the large library. In theory, except for the two cleaved sites, G20 and C21, we can generate 4²⁰ mutants totally.

Combining the bioinformatics and machine learning, we presented an algorithm to pre-processing our big mutation library. The flow chart of the pre-processing algorithm is shown below.




The SVM model was training well and the results were shown below.


After training the SVM model, we used it to evaluate the hairpin mutants. We selected the hairpin mutants with high ranks to check the four key points. Finally, we determined the five hairpin mutants below. The following chart shows the DR-Score which is the evaluated results from the SVM model.

Hairpin-Mutant	$DR-S\text{core}$
miniToe1	76.6306
miniToe2	65.6278
miniToe3	66.7160
miniToe4	62.5537
miniToe5	52.9794

After designing the protein mutants and hairpin mutants, we tested them in the wet lab.
And we try to gave a comparison between the special value we used before for evaluating the mutants and experimental results to check our model.

For the protein mutants, we gave a comparison between D₃ and experimental results.
As we can see in the Fig.17, we can find the inner relationship between D₃ and experimental results: the D₃ value describes the difference in the ability of cleavage between the wild-type and mutants. A higher D₃ value means a weaker cleavage ability.

For the hairpin mutants, we gave a comparison between DR-Score and experimental results.(Fig.18)
We can find the inner relationship between DR-Score and experimental results except miniToe 1. It is reasonable because the machine learning is quite sensitive to the data amounts and the R² is not 1 in our training result of SVM model.

Importantly, we tested 30 combinations of Csy4 enzymes and hairpins in wet lab.(Fig.19)

We have consturcted an coupled transcription-translation model to simulaiton the mRNA distribution in the origin time and final time of polycistron system. The Fig.20 and Fig.21 is the mRNA distribution in t=100s and t = 600s. The difference of two picture give us two information:

1.The different cistrons in diffrernt positions have different mRNA abundance.
2. The different cistrons in diffrernt positions have different translational time.

We have simplify the coupled transcription-translation model into a more flexible model to describe the dynamics of polycistron. This model is including four mian part, take an bicistron as an example:


(1)The transcription of two CDSs region:

Here we divided the polycistron into two part with different transcription paraments $k_1$ , $k_2$ to deal with the problem of different mRNA abundance due to the premature termination. The two paraments $k_1$ ,$k_2$ is totally sequence-dependent.

(2)The degradation of mRNA

The degradation of RNA also divided into two parts with different transcription paraments $k_{d1}$ , $k_{d2}$ to deal with the problem of different translational time for two mRNA. Each $k_{d\text{i}}$ can be divided into two part:
The $k_{\text{recoup}}$ denotes the recoup item for the translational time difference and the$k_d$ denotes the common degradation rate of mRNA.

(3)The translation of protein.
In the translation of two proteins, the two paraments used to describe the translation also should be different considering the translation coupling.

(4)The degradation of proteins

Our miniToe strucure can be used to protect the 5' end and 3' end of mRNA, which can be used to control the half-life of mRNA to control the ratio of expression level for cistrons in polycistron. As the Fig.22 show, the Csy4/RNA complex can protect the 5' end of mRNA. By choosing the differnt hairpin which has different binding capability, the mRNA will have different half-life.

Using the model constructed by OUC-China 2016, we explore the relationship between the cleavage rate and the ratio of two proteins in stable level. Fig.23 is the result of it.


From the Fig.23 we can find that the cleavage rate in our miniToe polycistron plays a role in changing the shape of product curve which have been proved in the first system, while have little effect in the ratio of two proteins in stable level.

Using the model constructed by OUC-China 2016, we explore the relationship between the cleavage rate and the ratio of two proteins in stable level. Fig.23 is the result of it.


From the Fig.23 we can find that the cleavage rate in our miniToe polycistron plays a role in changing the shape of product curve which have been proved in the first system, while have little effect in the ratio of two proteins in stable level.