5.1. Modeling
A previous study, 'Helix's Elasticity Study', shows that in order to form a coordinate system necessary for the calculation process, a two-dimensional figure must be created using atoms. The methods attempted in this study include a method to obtain elasticity by thinking of the template and auxiliary strands of DNA as individual helices, a method to create a two-dimensional figure by selecting the atom closest to a hydrogen bond, and C3, which is the end of each base. There was a way to create a two-dimensional figure using the midpoint, which is a virtual point. Among them, the method of thinking as an individual helix had the disadvantage that it may not take into account bending in DNA. In addition, the method using atoms close to hydrogen bonds has a disadvantage that the bending of the helical structure may not be considered. Therefore, the C3' atom was used as shown in [Fig. A virtual spiral is realized as shown in [그림 1] by using atoms of C3'. Using a virtual spiral, a two-dimensional slice was made as shown in [그림 1] and a coordinate system was formed. This focus gives different results from using atoms that are actually close to hydrogen bonds. The reason is that the bases are not kept in a straight line during simulation and are bent a lot. In this case, it is difficult to form a coordinate system that can obtain the elastic modulus even if the slice is composed.
Using the DCD file, which is the result of NAMD simulation, it is possible to obtain the coordinate values according to the timestep of the C3' carbons of deoxyribose in the nucleotide. Create an imaginary point using the midpoint of the C3' atom of the hydrogen-bonded base. A triangle formed by connecting three consecutive carbons among these virtual points is called a slice. The reason why the triangle is used as a slice here is that the coordinate system can be formed using the fewest points.
Let e_3 be the vector that takes the center of gravity of any slice as the origin and reaches the center of gravity of the next slice, and e' is the vector that connects the first and third carbons from the center of gravity of the slice to the bottom.
The neighboring coordinate system is related as the following equation by the rotation matrix.
The degree of change of the frame of the coordinate system is given by Frenet equations.
The solution of the above expression is given as
At this time, the interval between and is divided into subintervals of length delta s.
The duration l_p has the following relationship with this coefficient.
5.2. DNA implementation
5.2.1. DNA implementation through W3DNA and VMD
Random base sequence generation according to base ratio.
Using the python programming language with the base ratio of the template strand as shown in the table below, the base sequence is randomly arranged and the DNA base sequence with 20 base pairs is output.
| 주형가닥의 비율 | A(%) | T(%) | G(%) | C(%) | A, T(%) |
| DNA 1 | 10 | 20 | 30 | 40 | 30 |
| DNA 2 | |||||
| DNA 3 | 20 | 30 | 40 | 10 | 50 |
| DNA 4 | |||||
| DNA 5 | 30 | 40 | 10 | 20 | 70 |
| DNA 6 | |||||
| DNA 7 | 40 | 10 | 20 | 30 | 50 |
| DNA 8 |
Creating basic structures through W3DNA
Enter a random nucleotide sequence from W3DNA to construct a DNA PDB file.
DNA structure PDB, PSF file structure
Using VMD's autoPSF function, insufficient atoms (hydrogen) are added to the previously made incomplete DNA, and PDB and PSF files are created.
5.2.2. DNA solution file structure
Putting DNA in Water Box
Create a solvate file in which water molecules surround the DNA by using the solvate function of VMD for the PDB and PSF files of the DNA created earlier. A water box is necessary because dna is often with water in living things and acts as a force field in the simulation. The DNA should not be placed too close to the water interface. This is because when DNA approaches other DNA by periodic boundary conditions, they interact with each other and affect the simulation results.
Neutralizing DNA
In order to use the PME (particle mesh Ewald) function, the net charge of the molecular system must be zero. Since the net charge of DNA is not 0 due to the phosphate group, it is necessary to neutralize it. The Autoionize function in VMD can be used to obtain new PDB and PSF files with the addition of selected kinds of ions so that the net charge of the molecular systems in the PDB and PSF files is zero. In this study, an environment was created in which DNA was neutralized with sodium chloride (NaCl).
5.2.3. Parameter file and conf file creation (file required for simulation)
Modify parameter file
The parameter file required for simulation can be obtained from the downloaded VMD file. However, in this study, there was no specific parameter in the parameter file in the VMD file, so the modified file par_all36_na.prm and the par_water_ions.prm file were used together for simulation.
conf file creation
5.3. Simulation
In order to derive the elastic modulus and duration of DNA, data that can analyze the change over time of DNA is needed. Simulation to obtain change data of atoms constituting DNA.
5.3.1. Running NAMD2
Run the NAMD2 simulation from the command prompt.
5.3.2. DCD file
The DCD file created after the simulation is used for analysis.
5.4. Analysis
5.4.1. Analysis with VMD
5.4.2. Analysis with MATLAB
If we know the atomic number of C3' through VMD's TEXT EDITOR, we can find out what number it is printed in from DCD.
- Let the midpoint of the C3' atom of the base forming the hydrogen bond be the point constituting the slice.
- Composition of 3 slices
- Three orthogonal vector composition (e_1, e_2, e_3)
- Finding the Rotation Matrix U with the three vectors obtained above
- Using U to get Omega
- Finding w_1, w_2, w_3 using Omega
- Displaying the distribution of values of w_1, w_2, and w_3 as a histogram
- After normalization, the interval is selected so that the -log operation works well.
- Fitting with parabola
- Plot. And check whether the fit is correct with overlap
- Obtaining the elastic modulus (bending-modulus) and torsion (torsion: w) using the coefficient of the parabolic
- Equation obtained by fitting
5.5. Video production
In order to visually check the simulation results (changes in DNA), it is necessary to produce an image.
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