Team:EPF-Lausanne/Modeling overview

Minimization provides information that is complementary to molecular dynamics. Ensembles of structures are useful for calculating thermodynamic averages and estimating entropy, but the large number of structures makes detailed microscopic analysis difficult. Minimized structures represent the underlying configurations about which fluctuations occur during dynamics. Constraints are imposed during minimization.
To minimize we need a function (provided by the forcefield) and a starting set of coordinates. The magnitude of the first derivative can be used to determine the direction and magnitude of a step (i.e. change in the coordinates) required to approach a minimum configuration. To reach the minimum the structure must be successively updated by changing the coordinates (taking a step) and checking for convergence. Each complete cycle of differentiation and stepping is known as a minimization iteration.

The different steps are summarized and explained in our Analysis Methods section.
Our results can be found in the Results section.

In order to initiate molecular dynamics, velocities need to be assigned initially. This is done using a random number generator using the constraint of the Maxwell-Boltzmann distribution. The temperature is defined by the average kinetic energy of the system according to the kinetic theory of gases. The internal energy of the system is U = 3/2 NkT. The kinetic energy is U = 1/2 Nmv². By averaging over the velocities of all of the atoms in the system, the temperature can be estimated. It is assumed that once an initial set of velocities has been generated, the Maxwell-Boltzmann distribution will be maintained throughout the simulation.
Following minimization we can consider the temperature as being near zero Kelvin. To initialize dynamics the system must be brought up to the temperature of interest, that is 300K. This is done by assigning velocities at some low temperature and then running dynamics according to the equations of motion. After a number of iterations of dynamics, the temperature is scaled upwards. Since the velocity for each atom is distributed about an average of v = (3kT/m)^1/2 we can multiply all of the velocities by a common factor to obtain a new temperature. This is done systematically during the equilibration (initialization) stage.

PCA is a useful technique used for compression and data classification. The aim is to reduce the dimensionality (number of dimensions) of a data ensemble (sample), by finding a new set of variables with a smaller size than the original set of variables. However, this new set must contain the main part of the information: most of the information is kept in a smaller number of variables.
Information means variation in the sample, et given by the correlation between the original variables. The new variables are called principal components (PC), and are not correlated. They are given by splitting the total information contained in each one.