1. Introduction
This module shows how to work with a typical YUP model type: rrDNAv1. This module can be completed in seven hours.1. Introduction
2. Parameters
3. Create a Model
4. Molecular mechanics
5. Analyses
6. Saving your work
The first step in simulation is to build a model with an initial conformation. In 3DNA, we are interested primarily in the effect of linking difference on circular DNA of different size and degree of inherent curvature or lack of. Chapter 2 deals with building such models.
Once a model has been built, molecular simulations can begin. Typically, we will have to refine the initial structure and usually Energy Minimization is not sufficient. Thus, we used a technique called Simulated Annealing where we run a Molecular Dynamics simulation of the cooling of the DNA model. To check our simulations, we can visualize the final structure and verify that the topological quantities are as expected.
Each model type has an array of analysis techniques and a few are demonstrated in Chapter 5.
The 3DNA Model
We will use a reduced representation model of DNA for the exercises. This model has been implemented as part of the rrDNAv1 package. The standard parameter library for this model is Yup/Data/rrDNAv1/. The package directory is Yup/Models/rrDNAv1/.The rrDNAv1 model type includes DNA models at several reduced scales. Hybrid models that span several levels of representation can be built. However, we will use only the 3DNA model.
 |
The
3DNA model
represents each basepair of the DNA molecule with a plane formed by
three
atoms. These are located on one side of the base plane and are called
the center (C), front (F) and left (L) atoms.
The front and left atoms have no bulk while the center atom has a large
volume. The center atoms overlap to form a
barrier to strand
crossing. You can download a kinemage file of a 3DNA model from here and examine it closely with a viewer. The display items under the "3DNA" label show the entities that exist in a 3DNA model. The "Visual Aid" items show the entities that do not actually exist but are implied by the model. You can download a kinemage viewer from the Richardson Lab. at Duke. KiNG (tested) or Mage (not tested) should work. In the Harvey Lab., you can type the command "Yup.king ACGTACGTACG.kin". |
The following table lists the bonded interactions in one step of the sequence: among atoms of the current basepair (F, L and C) and with atoms of the previous basepair (F, L and C).
| Energy class | Interacting Atoms | Equilibrium Dimensions | |||
| Bonds | L | C | 5.0 Angstroms | ||
| F | C | 2.5 Angstroms | |||
| C | C | 3.4 Angstroms | |||
| Angles | L | C | F | 90 degrees | |
| L | C | C | 90 degrees | ||
| F | C | C | 90 degrees | ||
| C | C | L | 90 degrees + Tilt | ||
| C | C | F | 90 degrees + Roll | ||
| Impropers | L | C | C | L | Twist (symmetrical) |
The last two angle terms are called the tilt mimic and roll mimic respectively. These and the improper torsion interactions are assigned equilibrium dimensions based on the base types of the step. The numbers come from the Bolshoy DNA-bending rules. We do not endorse any particular rule: a DNA bending rule simply provides a convenient way to introduce inherent curves into a model. This then allows us to build models with homogeneous sequences (no inherent bending) or heterogeneous sequences (where we can control the location and degree of bending).
DNA Supercoiling
DNA over a certain size (a couple hundred basepairs) can be closed into a circle. The actual conformation of the DNA is not a flat circle, even if the DNA is perfectly relaxed when it is closed into a circle. The DNA is said to be circular because you can go round the molecule without encountering an open end.If, as is usually the case, the DNA is not relaxed (either before or after the closure), the molecule has an excess or deficit in winding. The molecule can respond to the winding difference by bending, i.e. supercoiling. This phenomenom is described mathematically by topological quantities: the Linking Number or Link (Lk), the Writhing Number or Writhe (Wr) and the Twisting Number or Twist (Tw). These numbers are related to each other by the Calugareanu Theorem: Lk = Wr + Tw. Lk can only be a whole number, Wr and Tw may be fractional.
For this tutorial, you only need to understand a few things about DNA supercoiling. As the winding difference is increased (in either direction), so does the energy. The circle of least energy is said to be at equilibrium linking and the specific linking difference is then zero. We usually construct an initial structure to have a perfectly circular conformation because it is easy to do. Wr for such a structure is zero. If we had put in a excess of winding the linking number will be higher than the equilibrium and the linking difference is positive. A deficit in winding leads to a lower than equilibrium Lk and a negative linking difference. In either case, the Linking Number must be preserved throughout a calculation. A change in Lk indicates that the model or the simulation has failed. A supercoiled structure has a non-zero Wr. Often, it is sufficient to look at the values of Lk and Wr to judge if a simulation is correct.
0. Preparations
1. Model Construction and Simulations
2. Programming with YUP Part 1
3. Programming with YUP Part 2
4. Force field Assembly
5. Developing Potential Energy Terms
1. Model Construction and Simulations
2. Programming with YUP Part 1
3. Programming with YUP Part 2
4. Force field Assembly
5. Developing Potential Energy Terms
Coming: additional exercises with the rrDNA model and a short exercise with the rrRNA model.
Yammp Under Python
The Harvey Laboratory
Python Home
Python Tutorial
(new browsers)