6.1. Graph(MATLAB)
The horizontal axis of the log omega graph means the torsion angle w_i, and the vertical axis means -ln(P(w_i)).
The graph should appear in the form of a parabola, but the bending modulus, twisting modulus, and intrinsic torsional values could not be derived because fitting was not performed well with the parabola. Instead, it was analyzed through graph reformation, using that the horizontal axis of the log omega graph is torsion w_i and the vertical axis is a value proportional to energy (beta is a constant since the temperature of the simulation environment is kept constant).
The w_i at the minimum point of the graph is the angle at which DNA is in stable equilibrium, and this can be regarded as the intrinsic torsion w_0i.
6.1.1. DNA 1(A, T ratio : 30%)
log omega1, log omega2 analysis
The slope is moderate around the stable equilibrium point of log omega1, but the slope becomes smaller as it deviates further to the left. The slope around each stable equilibrium point of log omega2 is similar to that around the equilibrium point of log omega1, but the slope is close to zero between the two stable equilibrium points. Through this, it can be seen that the degree of bending of this DNA in any direction is similar, and when it is bent over a certain angle, the elastic force approaches zero.
log omega3 analysis
The slope is large around the stable equilibrium point, and the slope has a negative value as it goes to the right. Through this, it can be seen that this DNA is difficult to twist, and if it is twisted over a certain angle, the elastic force acts in the opposite direction.
6.1.2. DNA 2(A, T ratio : 30%)
log omega1, log omega2 analysis
The slope is intermediate around each equilibrium point of log omega1, but the slope approaches zero between the two stable equilibrium points. Around the stable equilibrium point of log omega2, the slope is medium, but between the two equilibrium points, the slope is close to 0 and the interval is short. Through this, it can be seen that the degree of bending of this DNA in any direction in the equilibrium state is similar, and when it is bent over a certain angle at the stable equilibrium point, the elastic force approaches zero.
log omega3 analysis
To the right of the left stable equilibrium point, the slope is medium, and to the left of the right stable equilibrium point, the slope is large. In the center, the slope is close to zero. From this, it can be seen that this DNA has a stronger elastic force when the torsion is - than when the torsion is +.
6.1.3. DNA 3(A, T ratio : 50%)
log omega1, log omega2 analysis
Around the stable equilibrium point of log omega1, the slope is large and the interval is short. The more we deviate to the left, the smaller the slope. In the case of log omega2, it is similar to log omega1 except that the slope becomes smaller when it deviates to the right to some extent from the equilibrium point. Through this, it can be seen that the elastic force of this DNA is similar when bent in any direction, and the elastic force decreases rapidly when bent over a certain angle in a specific direction.
log omega3 analysis
The slope around the stable equilibrium point is small. Through this, it can be seen that this DNA has similar elasticity and weak elasticity no matter which direction it is twisted.
6.1.4. DNA 4(A, T ratio : 50%)
log omega1, log omega2 analysis
Around the stable equilibrium point of log omega2, the slope is moderate.
log omega3 analysis
The slope around the stable equilibrium point is moderate. From this, it can be seen that this DNA has a similar elasticity no matter which direction it is twisted, and that the elasticity is medium.
6.1.5. DNA 5(A, T ratio : 70%)
log omega1, log omega2 analysis
The slope is medium around the left of the stable equilibrium point of log omega1, and the slope approaches 0 as it deviates further to the left. The slope of log omega2 is small to the right of the stable equilibrium point, and the slope is large to the left of the stable equilibrium point. If it deviates to the right to some extent from the stable equilibrium point, the slope approaches zero. Through this, it can be seen that the elastic force of DNA 5 is different in each direction compared to other DNAs, and when bent over a certain angle in one direction, the elastic force approaches 0.
log omega3 analysis
The slope to the right of the stable equilibrium point is large, and the slope to the left is greater. To the right, the slope has a negative value. Through this, this DNA has a strong elastic force when twisted, and the elastic force when twisted in the clockwise direction is stronger than that when twisted in the counterclockwise direction. It can be seen that the elastic force acts in a clockwise direction.
6.1.6. DNA 6(A, T ratio : 70%)
log omega1, log omega2 analysis
Around the stable equilibrium point of log omega1, the slope is medium, and the section to the left is long. The further off to the left, the smaller the slope. The slope is large around the stable equilibrium point of log omega2, and when it deviates to the right to some extent, the slope approaches 0. Through this, it can be seen that DNA 6 has a stronger elastic force than other DNAs, and the elastic force is different for each direction in which it is bent.
log omega3 analysis
The slope around the stable equilibrium point is moderate.
6.1.7. DNA 7(A, T ratio : 50%)
log omega1, log omega2 analysis
The slope is small around the stable equilibrium point of log omega1. The slope is moderate around the stable equilibrium point of log omega2, but when it deviates to the right a little, the slope approaches zero. Through this, it can be seen that this DNA has weaker elastic force compared to other DNAs, the elastic force is different for each direction in which it is bent, and the elastic force decreases significantly when bent over a certain angle.
log omega3 analysis
The slope around the stable equilibrium point is moderate. From this, it can be seen that this DNA has a similar elasticity no matter which direction it is twisted, and that the elasticity is medium.
6.1.8. DNA 8(A, T ratio : 50%)
log omega1, log omega2 analysis
Looking at the graph of log omega1, the slope is medium. Looking at the graph of log omega2, the slope to the right of the stable equilibrium point is large.
log omega3 analysis
The slope around the stable equilibrium point is large. Through this, it can be seen that this DNA has similar elasticity and strong elasticity no matter which direction it is twisted.
6.2. Intrinsic Torsion Analysis
Since bending modulus and sustained length could not be obtained, analysis was performed using the fact that in log omega1, 2, 3 graphs, if the slope around the stable equilibrium point is steep, the elastic force is strong, and if the slope is gentle, the elastic force is weak.
Among intrinsic torsion values, the closer the values of w_01 and w_02 are to 0, the more the equilibrium state for DNA bending is a straight line. Also, as the value of w_03 is closer to 0, the equilibrium state against DNA twisting is a state in which the DNA is in an orthogonal view when viewed from above, as if 10 C3′s form the vertices of a regular decagon. The equilibrium state of DNA is a state in which the number of C3's is more than 10 when viewed from above as an orthographic projection. The values of w_01, w_02, and w_03 are w_01, w_02, and w_03 when the energy values are minimal because these values are in a state in which DNA is in equilibrium.
In the above equation, beta is a constant, so when the vertical axis value is the lowest in the log omega graph, the energy is the lowest, and the w_i value at this time is w_0i. When the shape of the log omega graph is a quadratic function, the values of alpha_1, alpha_2, and alpha_3 can be obtained by substituting the w_0i value in the equation below.
However, in this study, many of the graphs of log omega deviate from quadratic functions. It can be seen that the values of the bending elastic energy and torsional elastic energy of DNA have a different relationship than the quadratic function of bending and torsion. The reason for this is that, in the case of a single strand, the coordinate system influences each other and affects the U value, but it is interpreted that the DNA forms the coordinate system by selecting the midpoint in the double helix structure. Specifically, the movement directions of the main and auxiliary strands of DNA are different, so the movement of the coordinate system is inconsistent.
The table below shows the intrinsic torsion value (w_0i) for each DNA.
| w_01 | w_02 | w_03 |
|
| DNA 1 | 0.0575 | -0.0620, 0.0695 | -0.163 |
| DNA 2 | -0.0580, 0.1 | -0.0785~-0.0430, 0.0465 | -0.300~0.300 |
| DNA 3 | 0.0570 | -0.0760 | 0 |
| DNA 4 | 0.0915 | -0.037~0.00750 | -0.180 |
| DNA 5 | 0.0920 | -0.0735~ -0.0495 | -0.215 |
| DNA 6 | 0.0888 | -0.0830 | -0.233 |
| DNA 7 | 0.0710 | 0.100 | -0.204 |
| DNA 8 | 0.0225 | -0.0900 | -0.136 |
In this table, the range of values is written in the log omega graph format, since the minimum point is not visible and appears as a straight line, so the w_i values of both endpoints are respectively written down. It is small because there are two parts that are 'minimal').
DNA 1 and DNA 2, whose binding ratio between A-T and G-C are 3:7, respectively, have w_01 and w_02 values close to 0, except for 0.1 in w_01, indicating that they are straight. However, when comparing the w_03 value, the value of DNA 2 is larger than that of DNA 1. This shows that the DNA is somewhat twisted.
If we look at DNA 3 and DNA 4, where the ratio of A-T and G-C bonds are 1:1, it is difficult to find anything in common. Looking at DNA 5 and 6, where the ratio of A-T and G-C bonds is 7:3, respectively, w_01 is close to 0.1, indicating that the DNA is slightly curved, and looking at w_03, it is close to 0.2, indicating that the DNA is slightly curved. When looking at DNA 7 and 8, where the ratio of A-T and G-C bonds is 1:1, respectively, the w_02 value was similar, but the rest of the values did not. In particular, looking at the value of w_03, there is a difference of 0.1 between the two DNAs. Still, it can be seen that DNA 7 and 8 are bent to one side and slightly twisted. Looking at the DNA of Exploration 1, 2, 5, and 6, the ratios of A-T and G-C bonds are 3:7 and 7:3, respectively, and it can be seen that the higher the ratio of A-T bonds, the more curved and twisted in the general DNA structure. Therefore, the more A-T bonds, the smaller the elastic modulus of DNA.
6.3. Secondary research results and further research directions
6.3.1. Secondary research
In the results of the first study, it failed to obtain the elastic modulus and the sustained length, and succeeded in obtaining the elastic modulus and the sustained length by using a different research method. However, as a result of the secondary study, it was expected that similar values could be obtained theoretically in Explorations 1 and 2, Explorations 3 and 4, Explorations 5 and 6, and Explorations 7 and 8 with the same AT and GC binding ratios, but similar values were obtained. could not get In addition, the experimental values did not show a trend depending on the binding ratio, so no meaningful conclusions could be drawn. Therefore, based on the results of the secondary research, further research is planned to identify the problems.
6.3.2. Graph
A second study was conducted to obtain the modulus of elasticity that was not obtained in the first study. In the second study, simulation speed was increased by using a computer with built-in NVIDIA graphic card.(Workstation)
As the reason for not finding the elastic modulus in the first study, our team analyzed that it was a characteristic of DNA, which is a double helix structure. couldn't Therefore, this team analyzed that the results could not be derived by setting the frame : time (500 frame : 1 ns) ratio low in the first study. If the frame: time ratio is low, the change in DNA progresses rapidly, so it would not be appropriate for the method of this study to obtain the elastic modulus by measuring the change between coordinates. Therefore, this team conducted simulation by adjusting the frame:time ratio to (10000:1). As a result of the simulation, the following values could be derived.
6.3.3. Graph analysis
In the MATLAB code of the primary analysis, cut&norm omega was derived by cutting the data including data values belonging to the lower 20% of my omega. In this process, all data of matlab omega were reflected and derived. In the primary analysis method, even if there is a cut process, the phenomenon that affects a large amount of data such as temperature equilibrium does not occur properly or a vacuum bubble is generated cannot be eliminated. Also, data was imported symmetrically based on 0 in matlab omega, but only the part with data was used, so it was possible to see that the fitting was done to the quadratic curve in the last graph. In addition, if this method is used, the number of points used for fitting increases, so that the results can be better reflected.
6.3.4. Bending modulus, torsional modulus, intrinsic torsion
When the shape of the log omega graph is a quadratic function, the values of alpha_1, alpha_2, alpha_3, and w_0i can be obtained using the following formula.
6.3.5. Analysis 1
In the MATLAB code of the primary analysis, cut&norm omega was derived by cutting the data including data values belonging to the lower 20% of my omega. In this process, all data of matlab omega were reflected and derived. In the primary analysis method, even though there was a cut process, the log omega graph was not well fitted with a parabola, so bending modulus and intrinsic torsion could not be sufficiently derived.
| w_01 | w_02 | w_03 | |
| DNA 1 | 0.005 | NaN | 0.07 |
| DNA 2 | NaN | NaN | NaN |
| DNA 3 | NaN | NaN | -0.15 |
| DNA 4 | NaN | NaN | NaN |
| DNA 5 | NaN | -0.085 | NaN |
| DNA 6 | NaN | NaN | NaN |
| DNA 7 | 0.06 | NaN | -0.15 |
| DNA 8 | 0.038 | NaN | -0.14 |
6.3.6. Analysis 2
| alpha_1 | alpha_2 | alpha_3 | |
| DNA 1 | 17.9587 | 7.3289 | 12.5286 |
| DNA 2 | 245.0486 | 175.4222 | 36.8022 |
| DNA 3 | 60.2194 | 73.3273 | 2.2088 |
| DNA 4 | 428.7618 | NaN | NaN |
| DNA 5 | 314.5470 | 348.8872 | 93.7599 |
| DNA 6 | 261.9628 | 219.3839 | 36.0674 |
| DNA 7 | 307.3090 | 339.8549 | 61.0378 |
| DNA 8 | 68.2289 | 465.7206 | 33.3848 |
| w_01 | w_02 | w_03 | |
| DNA 1 | 0.004 | NaN | -0.208 |
| DNA 2 | 0.084 | -0.0649 | -0.25 |
| DNA 3 | 0.074 | -0.0321 | -0.14 |
| DNA 4 | 0.014 | 0.056 | -0.248 |
| DNA 5 | 0.082 | -0.078 | -0.147 |
| DNA 6 | 0.088 | -0.071 | -0.224 |
| DNA 7 | 0.061 | -0.0705 | -0.135 |
| DNA 8 | 0.042 | -0.082 | -0.144 |
| DNA 1 | DNA 2 | DNA 3 | DNA 4 | DNA 5 | DNA 6 | DNA 7 | DNA 8 | |
| l_p | 10.410 | 204.4706 | 66.1301 | NaN | 330.8284 | 238.7901 | 322.7636 | 119.021 |
l_p(Å) is the persistence length of DNA.
In the second study, the alpha_2 and l_p values of DNA 4 could not be derived. Also, in the case of DNA 1 in the secondary study, the l_p value is slightly different from 2, because a vacuum bubble was generated during the simulation process. In this case, it can affect the movement of DNA when the force is reflected in the periodic boundary condition. (It is possible that the ions added to the water box for neutrality had an effect.) Vacuum bubbles were formed in DNA 1 and 8, and since DNA 1 formed a larger vacuum bubble, a large difference in l_p was derived.
6.4. Further research direction
Change in the base sequence ratio
| 주형가닥의 비율 | A(%) | T(%) | G(%) | C(%) | A, T(%) |
| DNA 1 | 5 | 5 | 45 | 45 | 10 |
| DNA 2 | |||||
| DNA 3 | 15 | 15 | 35 | 35 | 30 |
| DNA 4 | |||||
| DNA 5 | 25 | 25 | 25 | 25 | 50 |
| DNA 6 | |||||
| DNA 7 | 35 | 35 | 15 | 15 | 70 |
| DNA 8 | |||||
| DNA 9 | 45 | 45 | 5 | 5 | 90 |
| DNA 10 |
- Quantitative analysis of bending modulus, intrinsic torsion, and continuous length
- Analysis of correlation between bending modulus and A, T ratio or number of hydrogen bonds
- Extension of simulation time : 5ns
- Design and conduct experiments to analyze the correlation between the strength of hydrogen bonds and the elastic modulus in the double helix structure
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