Mathematical Modelling of DNA
Supplementary Material for the first Lecture
Slides: Introduction to cgDNA
Here and here , you can download the slides shown in the introductory lectures of 20 and 24.2.2017 with much of the material to be discussed in further detail in later lectures, starting with the development of the cgDNA model on 6.3.2016.
Videos of atomistic models and MD simulations of DNA shown during lecture 1.
Linear DNA fragments::
3D view of the DNA , a 3D static view of the idealized highly twisted right handed double helical structure of a B-form DNA fragment with 15 base pairs.
DNA with water ,video of a fully atomistic molecular dynamics (or MD) simulation of a DNA fragment immersed in water. The molecules of water represent almost 90% of the total number of the atoms in the simulated system.
DNA with ions ,another video of a MD simulation of a DNA molecule where the green points represent only the charged ions in the solvent bath, water is in the simulation but is not shown in the visualisation. MD simulations of DNA are also used to understand the interaction between DNA and ions and the repartition of the ions around the DNA molecule.
Simulations of a DNA mini circle (i.e. a covalently closed loop of DNA):
Although it will not form a large part of the material in this course, in addition to being inherently multi-scale in both length and time scales, DNA also exhibits a multi-scale behaviour in different loading regimes. One way to strongly load DNA is to form short closed loops (or minicircles) which is a widely adopted experimental technique.
3D view of mini circle , a static 3D view of the structure of an almost circular DNA minicircle representing initial data at the beginning of a MD simulation.
Mini circle with ions , a visualisation of a segment (in time) of a molecular dynamics trajectory of the mini circle. For this simulation the total number of atoms (including water) was around 800K, so a system equivalent to approximately 5 million first-order ODE is being solved for approximately 10^8 time steps.
3D view of mini circle , this 3D view represents a final static snapshot of the simulation. One can notice that the mini circle has a straight part with kinks at either end where in response to the high (twist in this case) loadings the base pairs have unstacked to form kinks where the double helical structure of the DNA breaks down locally.
Physical model of DNA
A very coarse grain physical model of DNA. Oppositely oriented homogeneous sugar (red) - phosphate (purple) backbones linked by base pairs (GC, green-yellow, AT blue-orange) defining the sequence dependence. The two helical backbones are not diametrically opposed, leading to the formation of the evident major and minor grooves. Note that in this simple model the orientation of the backbones has been hidden. In effect the sugars are five element rings with four carbons and one oxygen. The location of the oxygen with respect to the four carbons in each sugar ring shows the so called 5'-3' direction of the backbone, but that level of detail is not present in this model. The anti-parallel orientation is visible in the 3D view of the DNA showing the ideal static B-DNA structure, because the five corner sugar rings have one red corner corresponding to the location of the oxygen in the ring.