Modeling overview
Protein domain of interest
Our protein of interest is LOVTAP. This protein was synthetically engineered by Pr. [http://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&cmd=search&term=18667691 Sosnick's] group from the University of Chicago. It is a fusion protein between a LOV domain (Avena Sativa phototropin 1) and the E. Coli tryptophan repressor.
This protein undergoes changes under light activation as shown by Sosnick et al, namely when the protein is activated by light it binds to DNA and inversely.
For more information about LOVTAP protein please click here.
Goal
Sosnick et al. found that light-activated LOVTAP isn't stable. After light excitation, the LOV domain returns to its ground state (non light-activated state) very quickly.
So the aim of the molecular dynamics simulation is to simulate the LOV domain in its environment under light activation (so-called light state) and without light activation (ground state, so-called dark state), calculate atom and residue movements of particular/interesting LOV domain regions, and finally deduce which residue(s) could be mutated to stabilize the light-activated state of this LOV domain (increase its lifetime).
Then, simulation of the complete LOVTAP protein with selected mutations could give us insights about the behavior of our protein in its environement.
Starting material
Both LOV domain crystallography files were obtained from [http://www.rcsb.org/pdb/home/home.do RCSB]:
- [http://www.rcsb.org/pdb/explore/explore.do?structureId=2V0W Light-activated LOV domain]
- [http://www.rcsb.org/pdb/explore/explore.do?structureId=2V0U Dark LOV domain]
These crystallographies were done by [http://www.ncbi.nlm.nih.gov/pubmed/18001137 Halavaty et al.].
Molecular dynamics: a little theory
Molecular dynamics simulation consists in the numerical, step-by-step, solution of the classical equations of motion. For this purpose we need to be able to calculate the forces acting on the atoms, and these are usually derived from a potential energy.
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This potential energy can be divided into:
The non-bonded interactions:
The Lennard-Jones potential is the most commonly used form, with two parameters: σ, the diameter, and ε, the well depth. It takes into account the Van der Waals forces. It represents the non-bonded forces and the total potential energy can be calculated from the sum of energy contributions between pairs of atoms.
Lennard-Jones pair potential showing the r−12 and r−6 contributions
when electrostatic charges are present, we add the Coulomb force, where Q1, Q2 are the charges and ϵ0 is the permittivity of free space
The bonded interactions:
Angles, bonds and dihedral angles have to be taken into account:
To understand a bit more, you can see the following article:
Introduction to Molecular Dynamics Simulation - Michael P. Allen
Steps
The following information is mostly taken from an Introduction to Molecular Dynamics: see [http://chsfpc5.chem.ncsu.edu/~franzen/CH795N/lecture/IV/IV.html here] their web page.
1. Minimization
Using the forcefield that has been assigned to the atoms in the system, it is essential to find a stable point or a minimum on the potential energy surface in order to begin dynamics. At a minimum on the potential energy surface, the net force on each atom vanishes.
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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.
2. Equilibration
Molecular dynamics solves the equations of motion for a system of atoms. The solution for the equations of motion of a molecule represents the time evolution of the molecular motions, the trajectory. Depending on the temperature at which a simulation is run, molecular dynamics allows barrier crossing and exploration of multiple configurations.
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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.
3. Analysis and validation
This part is dedicated to the analysis of our previous results, in order to validate the following researches. For more details about what we have done, see :
- the Analysis Methods page, which is composed of a step-by-step description of what we did : click here for more information on this topic.
- the Results page, which explain what we elicited from our raw data: click here for more information.
4. Simulation
We run a 100ns simulation, from which we will collect the data and see what happens to our protein! We made calculations during nearly 4 weeks, on 64 processors.
5. Atom movement analysis
In this last section we analyze the atom movement using the PCA analysis (Principal Component Analysis), for making predictive models.
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PCA is a useful technic used for compression and data classification. The aim is to reduce the dimentionality (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 spliting the total information contained in each one.
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