Team:OUC-China/miniToe Family

Team OUC-China: Main

miniToe Family

In the miniToe family, the protein and hairpin were mutated to meet the goal of the different regulation level. In this part, the model can help us design mutants. Importantly, we used different strategies to design the feature of Cys4 and the hairpin. For example, molecular dynamics played an important role in designing protein mutants, and the bioinformatics and machine learning supported us to find the hairpin mutants of our interest.

1. Enzymes Mutation

1.1 The Four Key POINTS in miniToe System

The wet lab members gave us four important sites, Gln104, Tyr176, Phe155, His29, which play important roles in binding and cleavage protein Csy4. Considering 20 kinds of amino acids, we have 80 mutants to explore and choose if we only have one site mutated.

Before designing the protein mutants, we looked into the working process of miniToe to find the most important key points in our system.

Fig.1-1 The working process of miniToe system

All the reactions happened in our first system, miniToe, can be described chronologically by following five main steps[1]:

(1)MiniToe is produced and accumulated.
(2)Csy4 is produced under IPTG conditions.
(3)Csy4 binds to the miniToe structure and forms Csy4-miniToe complex.
(4)Csy4 cleaves the specific site of miniToe structure into two parts: Cys4-crRNA (cis-repressive RNA) complex and mRNA encoding sfGFP.
(5)The sfGFP is produced.

There are four key points in our miniToe system, which confirms whether our system can work successfully;

(1)Does Csy4 dock correctly with the miniToe structure?
(2)How about the binding capacity between Csy4 and miniToe structure?
(3)How about the cleavage capacity between Csy4 and miniToe structure?
(4)Does cis-repressive RNA release from the RBS?

The most impressive way to explore four points is to model our system at the atom level by molecular dynamics[2]. And there are lots of work on exploring Csy4-crRNA complex by molecular dynamics[3][4][5].

1.2 Molecular Dynamics

Molecular dynamics (MD)[6] is a computer simulation method for studying the physical movements of atoms and molecules. The atoms and molecules allows to interact for a fixed period of time, giving a view of the dynamic evolution of the system. In most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, whose forces between the particles and potential energies are often calculated using interatomic potentials or molecular mechanics force fields.

For a system involving molecule or atoms, the total energy includes kinetic energy and potential energy，which can be described by the formula below:

E = E_{k i n} + U

where the E_kin denotes the kinetic energy and the U denotes the potential energy.

In a molecule system, the total potential energy can be calculated by adding the U_nb、 bond stretching potentials energy U_b、angle bending potentials energy U_θ、torsion angle potentials energy U_ϕ、out-of-plane potentials energy U_χ and some other cross effect U_cross together，which also can be described by the formula below:

U = U_{n b} + U_{b} + U_{θ} + U_{ϕ} + U_{χ} + U_{c r o s s}

This formula above is also called the force field in the theory of molecular dynamics. Based on the statistical thermodynamics and empirical result, there are many force field in the world. In the study of proteins and nucleic acids, the Amber force field is one of the best force field in the world. So we choose Amber as our force field and the formula of this field.

The items in the formula refers to bond stretching term、angle bending potentials、dihedral angle potentials、put of plane angle potentials、improper dihedral angle potentials、Van Der Waals interaction and Coulombic interaction terms in order.

Considering the system which contains N molecule or atoms in the classic mechanics, the atom or molecule can be characterized as follow:

The position of atom i is r_i , the speed of atom i is v_i , the acceleration of atom i is a_i.

After the integral operation, we can get two formula of v_i and r_i :

{\overset{⇀}{v}}_{i} = {\overset{⇀}{v}}_{i}^{0} + {\overset{⇀}{a}}_{i} t

{\overset{⇀}{r}}_{i} = {\overset{⇀}{r}}_{i}^{0} + {\overset{⇀}{v}}_{i}^{0} + \frac{1}{2} {\overset{⇀}{a}}_{i} t^{2}

where the v_i ⁰ refers to initial speed and the r_i ⁰ refers to initial position.

According to the classic mechanics, the force applied to atoms is the negative gradient of potential energy:

{\overset{⇀}{F}}_{i} = - \nabla_{i} U = - (\frac{\partial}{\partial x} \overset{⇀}{i} + \frac{\partial}{\partial y} \overset{⇀}{j} + \frac{\partial}{\partial z} \overset{⇀}{k}) U

Due to Newton’s second law, the acceleration of atom i can also be described as:

{\overset{⇀}{a}}_{i} = \frac{{\overset{⇀}{F}}_{i}}{m_{i}}

Using the total formula above together, we can have the full process of the molecular dynamics described and the Fig.2-2 shows the flow chart of MD in program.

Fig.1-2 The flow chart of MD in program

1.3 Logic Line

When choosing Csy4 mutants, we considered the four points that discussed before. We choosed the molecular dynamics as main tools to study our system in atom level. What's the logic line between them?

We considered the problems about choosing mutants in the following description:
In experiments strain-Csy4-Wide Type works well, proving that the four key points we discussed before was confirmed. The Cys4 in the strain-Csy4-Wide Type can dock correctly with the miniToe structure and the Csy4 have a good capacity of binding and cleaving miniToe structure, finally the cis-repressive RNA releases from the RBS. So we chose the strain-Csy4-Wide Type as a criterion, the four key points can be checked in all Csy4 mutants.

So there will be two main problems: How to describe the four key points in mathematics way and compare the wild-type Csy4 and mutant Csy4? That's what we discuss in the following two parts.

1.4 How to describe four key points in mathematical form

We are going to check the molecular dynamics of wild-type Csy4 in miniToe system and show how to describe four key points in mathematical form in this part.

For the first point, we defined a matrix called interaction matrix. It can describe the possibility of interaction between every amino acid of proteins and every nucleic acid of hairpins, this interaction matrix can be calculated by the catRAPID graphic[7]. We submitted the wild-type Csy4 and miniToe structure respectively to online service and it can return us the interaction matrix. The Fig.1-3 is the heat map of the interaction matrix for wild-type Csy4 in the hairpin region.

Fig.1-3 The heatmap of interaction matrix for wild-type Csy4.

And the rest three points is explained by the molecular dynamics. Some of our work about molecular dynamics is based on Jiří Šponer’s work[8], but most of work were done by us.

In order to explore the rest three key points, we prepared two structure for the molecular dynamics. The geometries of our miniToe system is based on the X-ray structure of Csy4/RNA complex with the cleaved RNA (PDB ID: 4AL5, resolution 2.0 A), it can be seen in the Fig.1-4.

Fig.1-4 the X-ray structure of Csy4/RNA complex

The first structure called precursor complex is prepared for the second and third point: how about the capacity of binding and cleavage between Csy4 and miniToe structure? The precursor complex consists of two part: wild-type Csy4 and miniToe structure. It describes the structure after the Csy4 bound to hairpin but didn’t cleave the hairpin in the special site. The Csy4 structure origins from the X-ray structure we mentioned before while the miniToe structure is constructed totally by the rational model: we put the sequence into the mFold[9] to generate the secondary structure of hairpin then the tertiary structure is produced by the RNAComposer[10]. The molecular docking between Csy4 and miniToe structure is carried out by PatchDock[11]. The precursor complex of wild-type Csy4 can be seen in the Fig.1-5

Fig.1-5. The precursor complex of wild-type Csy4

Having got the structure of precursor complex, we began to prepare for the simulation. Missing hydrogen atoms were added by PDBFixer[12], Forcefield we used is amber ff98SB[13]. The system is immersed in a rectangular TIP3P water box. After minimizing the energy of Protein/RNA system, we gave some restrictions on the RNA chain, making sure that the structure will not become an unreasonable structure when the temperature rises. All the reaction runs with the PBC condition under 300K and 1 atm in the NPT. The time step is 2 fs while the total simulation time is 50 ns. Gromacs[14] and OpenMM[15] are the most common software we used in Ubuntu 16.04 and Window10. The equipment we used is Intel i7 6700HQ with the NVIDIA GTX 960M 4G, it can simulate about 100-150 ns per day under the GPU acceleration. And the trajectories result is analyzed by Pymol[16] and MDAnalysis[17].

For the second point, what we can get from the simulation data is protein binding free energy used to describe the capacity of binding. The 20 ns data in the beginning is aborted. So we use the data in 30-50 ns, making sure the structure is smooth when calculating. The result of binding free energy for wild-type Csy4 is

△ G_{b i n d i n g} = - 59154.9251 \overset{}{} k j / mol

.

For the third point, what we can get from the simulation data is some significant distance of key interaction in the active site of Csy4, whicn describes the capacity of cleavage. Jiří Šponer[8] points out some important key interactions of the active site including Ser148(OG)-G20(O2’)、Ser150(OG)-G20(O3’)、Thr151(OG)-G20(N2’). Based on Jiří Šponer’s work, we finally chose the Thr151(OG)-G20(N2’) as our mathematical form in the third point. The distance curve of Thr151(OG)-G20(N2’) for wild-type Csy4 can be seen in Fig.1-6. We get the similar result compared to Jiří Šponer’s work[8].

Fig.1-6. The distance of Thr151(OG)-G20(N2’) in wild-type Csy4

The second structure called product structure is prepared for the fourth point: does cis-repressive RNA release from the RBS? The product complex consists of two part after cleavage: wild-type Csy4 and miniToe structure. It describes the structure after the Csy4 binding and cleaving the hairpin in the specific site. The Csy4 structure comes from the X-ray structure we mentioned before while the miniToe structure is designed totally by the rational model: we put two RNA sequence into the SimRNAweb[18] to finish the molecular docking of two chains RNA and generate the tertiary structure. And the molecular docking between Csy4 and miniToe structure is carried out by PatchDock[11]. The product complex of wild-type Csy4 can be seen in the Fig.1-7

Fig.1-7 The product complex of wild-type Csy4

We also explore the product complex by molecular dynamics following the protocol mentioned before. But in this part, we only set restrictions on RBS chain while the crRNA chain is free in moving.

For the fourth point, what we can get from the simulation data is the RMSD. It can describe the movement of the crRNA chain in a mathematical form. We can see the RMSD in Fig.1-8. The RMSD is unstable and it explains that crRNA released from RBS.

Fig.1-8 The RMSD of the product complex of wild-type Csy4

1.5 How to compare four mathematical forms between wild-type and mutants

We are going to check the molecular dynamics of the miniToe system with Csy4 mutants to show how to compare the four mathematical forms we chose before between the wild-type Csy4 and Csy4 mutants. In the following description, we give an example using the mutant Q104A to show you how to compare.

Fistly we use the SwissModel[19] to generate the tertiary structure with the template Csy4 (PDB ID: 4AL5, resolution 2.0 A). Using the molecular dynamics, we can get four mathematical forms showing in the Fig.1-9.

Fig.1-9 The four key points in mathematical forms for Csy4-Q104A

Now we divided the four curves into two kinds of data: the matrix and the numerical value. The interaction matrix and the curve can be regard as matrix because the curve is discrete, and the binding free energy is just an numerical value.

For the matrix we can use Euclidean distance to describe the differences between two matric:

D (p, q_{W T}) = \sqrt{\sum_{i}^{m} \sum_{j}^{n} {(p_{i, j} - q^{W T}_{i, j})}^{2}}

For the free bind ing energy, we can use the formula below to calculate the differences between the wild type and mutant[20]:

\ln (K_{d r e l}) = \ln (\frac{K_{d W T}}{K_{d M U T}}) = △ △ G_{b i n d i n g}

According to the descriptions above, we defined four values that used to compare four key points between mutant and wild-type:

D_{1} (int t e r a c t i o n \overset{}{} m a t r i x)

,

\ln (K_{d r e l})

,

D_{3} (T h r 151 - G 20 \overset{}{} c u r v e)

,

D_{4} (R M S D)

.

For the mutant Q104A, the four values shows in the following chart

Csy4-Mutant	$D_{1}$	$\ln (K_{d r e l})$	$D_{3}$	$D_{4}$
Q104A	0.483	2483	9.48	30.82

1.6 Conclusion and Result

From discussions in 1.4 and 1.5, we had the tools to evaluate the four key points in mathematical form and found the method to compare the mutant and wild-type. The next step is to find out the mutant that meets our needs.

We chose the top 10 mutants in D₁ to explore the molecular dynamics. And we mainly focused on the D₃ which describes the capacity of cleavage while the D₄ and ln(K_rel) is an alternative value to be considered. And the value of D₃ need to be limited to make sure the mutant which is totally inactive in cleavage won't be chosen. Luckily, we find that the Csy4-H29A is an inactive protein which has been proved[21]. So we chose 13.41, which is the D₃ value for Csy4-H29A as the threshold.
According to what we have discussed, the five mutants were chosen in the following table:

Csy4-Mutant	$D_{1}$	$\ln (K_{d r e l})$	$D_{3}$	$D_{4}$
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

2. Hairpin Mutation

2.1 The Large Mutant Library

Starting with the hairpins we want to design. We knew that the hairpin used in miniToe structure comes from the Repeat Area in CRISPR type I-F system. It can be recognized and cleaved by Csy4, and it is also called DR in CRISPR system. The Fig.2-1 shows a stander CRISPR array. The yellow line between two DR is guide RNA（gRNA）which is caught from foreign DNA[22].

Fig.2-1 the structure of CRISPR Array

When designed the hairpin mutations, it is impossible to use the MD method to find out which hairpin can meet our needs because the mutation library is too large. In our miniTioe structure in Fig.2-2, except for the two important bases----G20 and C21, the mutant library is about 4²⁰. If we still use molecular dynamics to explore all the hairpin mutations, too much time and lots of computer resources will be wasted.

Fig.2-2 The structure of miniToe

2.2 Pre-processing Algorithm

Combining the bioinformatics and machine learning, we present a pre-processing algorithm for our big mutation library. Fig.2-3 is the flow chart of the pre-processing algorithm.

Fig.2-3 The flow chart of this pre-processing algorithm

The first step of pre-processing algorithm is to find all the repeat areas in the genome as training input. We download the genome as much as possible from NCBI. With the help of PILER-CR[23], an algorithm that used to find the Repeat Area in bioinformatics, we can get the Repeat Area and CROSPR array from genome quickly. And we only focus on the Repeat Area whose length are 28 and 29 bp because Some researches show that the length of Repeat Area in CRISPR type I-F system are 28 and 29 bp[24]. In the first step, we download about 5000 genomes and find out 119 Repeat Areas which are 28 and 29 bp. The Fig.2-4 shows the 48 Repeat Areas whose length is 28 bp we find.

Fig.2-4 The Repeat Area which is 28bp

The second step of pre-processing algorithm is to score the hairpin we get in the first step. We created a score called DR-Score to evaluate the quality of Repeat area comparing to the wild-type hairpin. The calculation method is below:

{DR-Score}^{i}_{P A} {=E}_{H} • \sum_{n} \frac{D R_{size} + N_{mismatcn}}{D R_{size}}

This formula can be divided into two parts. The first part is E_H , regularized Levenshetein Distance value between evaluated hairpin and wild-type hairpin, which is an index to describe sequence similarity in bioinformatics. The second part is possibility value,$\sum\limits_{\text{n}} {\frac{{D{R_{{\text{size}}}}{\text{ + }}{N_{{\text{mismatcn}}}}}}{{D{R_{{\text{size}}}}}}} $, which describes the quality of Repeat areas in the genome on its own. DR_size refers to the length of Repeat Area, which is 28 or 29 bp in this case. The N_mismatch refers to the number of mutated nucleic acids in Repeat Area in the CRISPR array compared to the common one. The n refers to the times that the common Repeat Areas apereas in the CRISPR array.

Now take the CRISPR loci in Fig2-5 as an example to calculate the possibility value.

Fig.2-5 one CRISPR array comes from CRISPR database

The CRISPR array shows in Fig.2-5 has 9 Repeat Areas which contains 3 kinds:

DR1: ‘ACTGTACCATGCCTTACTTTGGATTCAAGGCAAAAC’

DR2: ‘ACTGTACCATGCCTGATTTTGGATTCGAGGCAAAAC’

DR3: ‘ACTGTACCATGCCTTACTTTGGATTCAAGTAAATCG’

The first Repeat area is most common while the rest has some mutation. The 3 possibility values are listed following:

D R 1 - P o s s i b i l i t y V a l u e = \sum_{n} \frac{D R_{size} + N_{mismatcn}}{D R_{size}} = \sum_{9} \frac{36 + 0}{36} = 9

D R 2 - P o s s i b i l i t y V a l u e = \sum_{n} \frac{D R_{size} + N_{mismatcn}}{D R_{size}} = \sum_{9} \frac{36 + 3}{36} \approx 1.083

D R 3 - P o s s i b i l i t y V a l u e = \sum_{n} \frac{D R_{size} + N_{mismatcn}}{D R_{size}} = \sum_{9} \frac{36 + 5}{36} \approx 1.14

It is quite easy to understand why the DR-Score is divided into two part. We need the Levenshtein Distance to describe the sequence similarly because not just the length of Repeat Area in CRISPR type I-F system is 28 and 29 bp[26], we need it to distinguish the hairpins which is totally faulted. And we also need the possibility value to describe the quality of hairpins we get, and it is constructed by the following assumptions: the more you occur, the better you are.

And If the same Repeat Areas occurs in j different species，we use the weight means to calculate the DR-Score. Just assume that there are n_i repeats in the in the i th species, the DR-Score can be calculated by the formula below:

D R - S c o r e = \sum_{i = 1}^{j} (\frac{n_{i}}{\sum_{m}^{j} n_{m}} D R - S c o r e_{i})

The third step of pre-processing algorithm is training the SVM model. The SVM (support vector machine) is a machine learning algorithm which is used to classify and regress[25]. It can construct the complex relationship between input and output with the help of kernel function. And it has been successfully used in predicting the strength of promoter. In this step, we chose the sequence of Repeat Area as input and the DR-Score as output.

Before we trained the SVM model, we should first change the sequence into mathematical representation using the following method.
The original sequence data Seq='seq1seq2...seqn-1seqn' which is coded by 'A', 'G', 'C'and 'T' can be transformed into the matrix x by the formula below:

x = {\begin{cases} [1, 0, 0, 0] \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} s e q_{i} = A \\ [0, 1, 0, 0] \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} s e q_{i} = G \\ [0, 0, 1, 0] \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} s e q_{i} = C \\ [0, 0, 0, 1] \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} \overset{}{} s e q_{i} = T \end{cases}

For example, the ‘AGCTA’ can be transformed into the matrix: [1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,1,0,0,0] .

After processing the sequence data, we divided the data into two part: training data and test data, then tried to train the model.

The complex relationship between the Repeats sequence matrix x and its DR-Score y can be mapped by an SVM regression function y=f(x). In order to achieve our goals, the SVM model is constructed following Vapnik et al[25]:

The performance of the SVM model is evaluated by two Squared correlation coefficient (R²)：

R^{2} = \frac{{(n \sum_{i = 1}^{n} f (x_{i}) y_{i} - \sum_{i = 1}^{n} f (x_{i}) \sum_{i = 1}^{n} y_{i})}^{2}}{(n \sum_{i = 1}^{n} f {(x_{i})}^{2} - {(\sum_{i = 1}^{n} f (x_{i}))}^{2}) (n \sum_{i = 1}^{n} y_{i} - {(\sum_{i = 1}^{n} y_{i})}^{2})}

The f(x_i) and y_i are the values of the prediction and of DR-score of the Repeat. Many kernel functions have been tested including polynomial function, the sigmoid function and Gaussian radial basis function (RBF). The RBF is the best choice of our model finally. Fig.2-6 shows the training results by giving the R² of training data and testing data which both have high R².

Fig.2-6 The training result

The last step of pre-processing algorithm is to evaluate the big mutation library using the SVM model we trained in the third step before. And by the model we can give a score to the hairpin.

2.3 Re-Check and Result

After pre-processing the big mutant library, we chose 10 hairpins whose scores are high but also in gradient, which can make sure that we can achieve the goal of different expression level. Then we re-check the four key points to
All in all, we finally chose five hairpin mutants in the following chart:

Hairpin-Mutant	$D R - S core$
miniToe1	76.6306
miniToe2	65.6278
miniToe3	66.7160
miniToe4	62.5537
miniToe5	52.9794

3.Comparing to the experiment

After designing the protein mutants and hairpin mutants, the wet lab members tested the all the Csy4 mutants and hairpin mutants. The result can see in the Fig.3-1.

Fig.3-1 The experimental result of mutants

And we tried to give 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. Fig.3-2 is the results.

Fig.3-2 The comparison between model and experiment for protein mutants

As we can see in the Fig.3-2, we can find the inner relationship between D₃ and experiment results: the D₃ value describes the difference in the capacity of cleavage between the wild-type and mutant. The higher D₃ value means that it will have weaker capacity of cleavage than the wild-type Csy4.

For the hairpin mutants, we gave a comparison between DR-Score and experimental result. Fig.3-3 is the result.

Fig.3-3 The comparison between model and experiment for hairpin mutant

As we can see in the Fig.3-3, we can also find the inner relationship between DR-Score and experiment results except for the 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.

After all, our wet lab member test 30 combinations of our Csy4 and hairpin. Fig.3-4 is the heatmap result of it.

Fig.3-4 The heatmap results of 30 combination

4.Future Work

1) The QM/MM molecular dynamics is used to design protein mutants more frequently[26], we are going to use it to explore more details in Csy4/RNA complex.And there are something out of Intuitive you can see in the Fig.3-4. For example the high expression of miniToe4-H29A. I think it may be described with the QM/MM molecular dynamics method.

2) We are going to find more Repeat Areas to increase the data amounts for our pre-processing algorithm.

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