DNA-like molecules with random dissociation
Channel: Nils Berglund
Date: 19/04/2024

In this variant of the simulation https://youtu.be/o_E5AHa0VH0 featuring a simple model for DNA formation, several rules have been added to avoid the formation of "damaged" DNA, consisting for instance of two nucleotides attaching at two different points. In addition, nucleotides have a small probability to detach at random times, to give badly built DNA strands a chance to improve. 
Each T-shaped molecule in this simulation represents a nucleotide, consisting of a phosphate-deoxyribose backbone, and one nucleic base among adenine (A), thymine (T), guanine (G) and cytosine (C). Atoms belonging to different molecules interact via a Lennard-Jones potential, while atoms within the same molecule interact through a stiff harmonic potential. Whenever two ends of T-bars come close to each other, they "react" to become attached. In a similar way, adenine and thymine can attach to each other, as well as cytosine and guanine.
Each reacting extremity of a nucleotide consists of two atoms. This provides more rigidity to the larger molecules formed after reactions. The left and right ends of each backbone are considered as being different, and can only attach to a backbone end of the other type. This is to avoid that base pairs point in different directions (a problem that is specific to the 2D nature of this simulation). 
Compared to the previous simulation https://youtu.be/o_E5AHa0VH0 , several rules have been added to make reactions possible. One of them is that if two nucleotides attach via the backbone, they cannot attach via the bases as well, and vice versa. Another rule is that each "end" of a nucleotide can only attach to the end of another nucleotide. This avoids situation where three different nucleotides are attached via their backbones, or via their nucleic acids.
The video has two parts, showing the same simulation with two different color schemes:
Type: 0:00
Orientation: 2:01
In the first part, the particles' color hue depends on their type. The base types appear in the following colors: A red, T yellow, C green, G cyan. In the second part, it depends on their orientation. 
To save on computation time, particles are placed into a "hash grid", each cell of which contains between 3 and 10 particles. Then only the influence of other particles in the same or neighboring cells is taken into account for each particle. 
The temperature is controlled by a thermostat, implemented here with the "Nosé-Hoover-Langevin" algorithm introduced by Ben Leimkuhler,  Emad Noorizadeh and Florian Theil, see reference below. The idea of the algorithm is to couple the momenta of the system to a single random process, which fluctuates around a temperature-dependent mean value. Lower temperatures lead to lower mean values. 
The Lennard-Jones potential is strongly repulsive at short distance, and mildly attracting at long distance. It is widely used as a simple yet realistic model for the motion of electrically neutral molecules. The force results from the repulsion between electrons due to Pauli's exclusion principle, while the attractive part is a more subtle effect appearing in a multipole expansion. For more details, see https://en.wikipedia.org/wiki/Lennard-Jones_potential

Render time: 26 minutes 18 seconds
Compression: crf 23
Color scheme: Part 1 - Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Part 2 - HSL/Jet

Music: "Lunar Landing" by Silent Partner

Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). https://doi.org/10.1007/s10955-009-9734-0
http://www.maths.warwick.ac.uk/~theil/HL12-3-2009.pdf

Current version of the C code used to make these animations: 
https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)

#molecular_dynamics #dna