Nils Berglund | DNA-like molecules in a box @NilsBerglund | Uploaded May 2024 | Updated October 2024, 6 minutes ago.
This simulation of a simplified model for DNA-like molecules uses the same parameter values as in the video youtu.be/EHx54yYnT7Y , but the periodic boundary conditions have been replaced by boundary conditions confining the molecules to a rectangular box, in order to avoid the "flying ice cubes" effect that occurred in the previous simulation.
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 with 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). The temperature is slowly increased during the simulation. This is because otherwise the system tends to "freeze", probably due to energy being absorbed in small vibrations within the molecules.
Whenever an A base comes close to an A, C or G base, the nucleotide containing that base separates from all other nucleotides. Similar rules apply in all other situations that differ from the allowed connections A-T and C-G. This makes it less likely that "damaged" strains of DNA form, containing gaps due to non-matching pairs facing each other. In addition, Coulomb-like interactions between base pairs and backbone ends have been added, which are attractive for pairs that can combine, and repulsive otherwise.
The video has two parts, showing the same simulation with two different color schemes:
Type: 0:00
Orientation: 1:41
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 en.wikipedia.org/wiki/Lennard-Jones_potential
Render time: 50 minutes 47 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: "I've Just Had an Apostrophe!" by Spazz CardiganSpazz Cardigan - Topic
Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). doi.org/10.1007/s10955-009-9734-0
maths.warwick.ac.uk/~theil/HL12-3-2009.pdf
Current version of the C code used to make these animations:
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
This simulation of a simplified model for DNA-like molecules uses the same parameter values as in the video youtu.be/EHx54yYnT7Y , but the periodic boundary conditions have been replaced by boundary conditions confining the molecules to a rectangular box, in order to avoid the "flying ice cubes" effect that occurred in the previous simulation.
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 with 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). The temperature is slowly increased during the simulation. This is because otherwise the system tends to "freeze", probably due to energy being absorbed in small vibrations within the molecules.
Whenever an A base comes close to an A, C or G base, the nucleotide containing that base separates from all other nucleotides. Similar rules apply in all other situations that differ from the allowed connections A-T and C-G. This makes it less likely that "damaged" strains of DNA form, containing gaps due to non-matching pairs facing each other. In addition, Coulomb-like interactions between base pairs and backbone ends have been added, which are attractive for pairs that can combine, and repulsive otherwise.
The video has two parts, showing the same simulation with two different color schemes:
Type: 0:00
Orientation: 1:41
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 en.wikipedia.org/wiki/Lennard-Jones_potential
Render time: 50 minutes 47 seconds
Compression: crf 23
Color scheme: Turbo, by Anton Mikhailov
gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a
Music: "I've Just Had an Apostrophe!" by Spazz CardiganSpazz Cardigan - Topic
Reference: Leimkuhler, B., Noorizadeh, E. & Theil, F. A Gentle Stochastic Thermostat for Molecular Dynamics. J Stat Phys 135, 261–277 (2009). doi.org/10.1007/s10955-009-9734-0
maths.warwick.ac.uk/~theil/HL12-3-2009.pdf
Current version of the C code used to make these animations:
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
