|
Molecular Dynamics of Lipid Aggregates
Lipid aggregation can be well explained by the mutual repulsion of water and the
hydrocarbon chain that forms the hydrophobic tail of lipid amphiphiles.
Furthermore, Van-der-Waals interactions between the unpolar tails might be
important for micelle formation. Both repulsion and Van-der-Waals forces can be
expressed by pairwise potentials between the involved particles. The most common
potential function has been introduced by Lennard and Jones and reads
where r denotes the distance between two particles and ε
and σ the stength and range of repulsion with respect to their
hydrophilic properties.
The pairwise potentials add up to an overall potential Ui for
each particle i in the system. In addition, two particles can be
covalently bonded. If so, a quadratic expression denotes the bonding potential
and is added to the above sum.
Given the potentials of all particles, we use Netwon dynamics to model their
motion. In addition, friction and thermic noise describe the medium in which
particles move. This leads to an ordinary second order differential equation for
each particle:
whereby xi, vi denote position and velocity
of particle i, mi its mass and Ui the
potential with respect to the positions of other particles. γ is
the friction coefficient of the medium, ξσ is a
Gaussian distributed random vector. Particle motion is calculated by a stepwidth
adaptive Euler approximation.
In order to explore the kinetics of chemical reactions, the tool allows the
user to define arbitry particles and reactions between them.
After each timestep, reaction probabilities are determined for all pairs
of reactants within a predefined critical range. These probabilities depend on
particle distances as well as the distance of eventually present catalysts. If a
reaction occurs, reactants are exchanged by products.
Figure 1:
Main window of the tool showing the particle space and time evolution of
potential and kintetic energies.
Figure 2:
The user can define particles and reactions via a graphical settings dialog.
Apart from this, potential functions can be redefined in the settings dialog
by writing short functions using Python programming language.
The program offers both visual and numerical output. The user can choose
analyses to perform from a wide palette of different observables like potential
and kinetic energy, particle numbers, micelle size distributions, a.s.o.
Further developpment of the tool will allow distributed computation.
| 
Research Project from the ICREA/Complex Systems Lab 
