Team:TU Darmstadt/Modeling MD

Molecular Dynamics

Molecular dynamics (MD) is one of the most common tools in computational biology. MD simulations solve the classical newton’s equations of motion. For the computation we need to calculate all forces acting in our system. The Forces are described within a potential energy -the Force Field and depends on the atomic coordinates r. For the illustration the potential is computed as follows:

The first term represents a a Lennard-Jones (LJ) potential. It approximates the interaction between a pair of neutral atoms or molecules. The second term is a coulomb potential between a pair of atom I and j. The last terms describe bonds and angles potentials. Due to experimental data and quantum chemical calculations the force-field parameters can be identified.The quality of MD simulations is mainly depending on the applied force field. In physics, a force field is a vector field which describes range dependent all non-contact forces acting on a particle. Applied in biochemistry a force field is a collection of mathematical functions and parameters which describe the potential energy of particles (atoms and molecules) in a defined system. For our simulations we used the AMBER (Assisted Model Building with Energy Refinement) force field which was especially developed to describe proteins and DNA.

Goal

In order to characterize the enzyme construct and to simulate its complex behavior, MD was required to study the interactions. Hence to the degradation of PET, our Team designed a sophisticated protein-construct. This construct is a fusion protein containing a degradation module (PDB :1CEX, pnB) and EstA (PDB id: 3KVN), a membrane bounded beta-beryl. Moreover, this construct is exposed at the outer membrane of our bacteria. Hence, we quantified the dynamic nature of our degradation protein with coarse-grained methods we have to quantify the motion within this construct surrounded by its native environment. We firts have to create a scene were we put our fusion protein and put it into a membran layer. Although simulating this fusion protein was indispensable, it seems to be a complicated task.

Methods

We used Yasara Structure simulation protocol for membrane protein. But we changed parameters and settings to fit it with our fusion protein-construct.

In the beginning we have our protein in an empty space, so we put a box around it. Moreover, we have to define our system and set some simplifying constrains: First we define our system as isolated from the surrounding, so that there is a constant number of a particles (atoms), volume of the simulation box and the temperature is limited in a defined range. Further more the simulated volume is periodic, that means if one particle leaves the volume on the one side, it simultaneously enters the volume on the opposite side.

Protocol for the simulation of 1CEX fused with 3KVN in lipid layer

Setting the Parameters =

• Forcefield: AMBER03
• Periodic simulation box
• Membrane composition: 100 % phosphatidyl-ethanolamine (PEA)
• Equilibration period = 250 ps
• duration= 3.5 ns
• temperature= 298K
• Membrane height = 43 nm
• Height of the hydrophobic membrane core = 28 nm
• Periodic simulation box
• duration : 5 ns

Flow

• scanning the protein for hydrophobic aa
• calculate the size of the membrane
• make a short MD Simulation of the membrane
• insert the protein into the membrane
• Adding water to the Scene
• Performing pH neutralization experiment
• Energy Minimisation
• keep the Protein rigid
• Equilibration of the solvent
• Equilibration of the membrane
• Protein free and simulating

Now we are ready to start the simulation. For each of the molecules in our simulation element we solve the equation from above and find out the forces which act on them. Then the forces were applied on the molecules for a short time period (femto seconds; fs) which results in a movement. A snapshot is taken of each atom position and the whole calculation starts over again. Doing this calculation for several of thousand times the result is a motion study of all atoms in the simulation box, a MD simulation.

Analytics

RMSF

The Root mean square fluctuation (short: RMSF) can be computed as followed:

where T is the duration of the simulation (time steps) and xi(tj) the coordinates of atom xi at time tj. Now we are calculating the sum of the squared difference of the mean coordinate xi and xi(tj) . Furthermore we divide the sum to T and extract the root of it. Hence we are able to calculate the fluctuation of an atom with its mean in trajectory files. The RMSF was computed from the atomic coordinates of the C-alpha in R using the bio3d library.

RMSD

The Root mean square deviation (short: RMSD) can be computed as followed:

where n is the number of atoms (C-alpha or backbone atoms). Vi is defined as the coordinates of protein V atom I. Here, the RMSD is used to quantify a comparison between the structures of two protein (v and w) folds .The RMSD was computed from the atomic coordinates of the C-alpha in R using the bio3d library.

Results

1CEX fused with 3KVN in lipid layer

3KVN in lipid layer