The coiled-coil is one of the most important aspects of our project. It is what enhances our proteins beyond than being just pretty constructs, but functional units in a working biosensor. Using 35 residue coils with five-heptad repeats containing a hydrophobic core and electrostatic tail interactions, our two coils readily associate together spontaneously. As we were unable to gain access to a laboratory over the summer, it was imperative that we tested the stability of our coils one way or another. Upon our exploration of the molecular dynamics suite GROMACS, we discovered a technique known as Umbrella Sampling and began conducting simulations.
Umbrella sampling is a technique used to calculate potential of mean force (PMF) to study protein binding-unbinding interactions. The PMF can then be used to derive the binding energy (ΔGbind). Umbrella sampling is conducted by generating an initial series of configurations corresponding to a location where one of the coils is harmonically restrained at increasing center-of-mass (COM) distance from the other coil through an umbrella biasing potential. The restraint placed upon one of the coils promotes it to sample the configurational space in a defined region along a reaction coordinate defined between the two coils. The result of this sampling is a derivation of the ΔGbind between the two coils.
Step 1. Generate the Protein Topology
After importing the coiled-coil construct files into GROMACS, the protein topology was generated. The topology contains the defining characteristics of a protein within a simulation, including nonbonded (atom types, charges) and bonded (bonds, angles, dihedrals) parameters. It also contains a force field, which is a collection of equations and associated constants that attempt to recapitulate the physical characteristics of a protein. The PLS-AA/L all-atom force field was used for our models.
Step 2. Create and Solvate a Box (Environment Generation)
For our modelling purposes a simple aqueous system was generated. This involved defining a box that would contain our FBP constructs, and then systematically filling the box with water molecules.
Step 3. Neutralizing System Net Charge
The solvated system we had created contains our charged coiled-coils construct. This net charge can lead to several artifacts and inaccuracies in the simulation; therefore, it was neutralized by adding ions. We systematically added Na+ and Cl- ions to the solvation to neutralize any charge that was present in the protein.
Step 4. Energy Minimization
We have now created a solvated, and electroneutral system. To ensure there were no steric clashes or misfolding in our constructs we performed structural relaxation through energy minimization.
Step 5. Isothermal-Isochoric Equilibration To avoid system collapse and begin performing the molecular dynamic simulations, the solvent and ions were equilibrated around the protein. This was done by equilibrating the system on the basis of temperature to ensure proper orientation of the protein.
Step 6. Isothermal-Isobaric Equilibration
This step is almost identical to Step 6 except the system was equilibrated and stabilized on the basis of pressure and density instead of temperature.
Step 7. Generating Configurations
To begin conducting the umbrella sampling simulations, a series of configurations along a reaction coordinate were generated. These configurations serve as the initial configurations for the umbrella sampling windows, which are run as independent simulations.
Step 8. Perform Umbrella Sampling Simulations
Once the initial configurations (Step 7) were identified and generated, the umbrella sampling simulations were conducted.
Results and Interpretation
After preparing our system containing the coiled-coils for umbrella sampling, we had to generate an initial series of configurations along a reaction coordinate (as discussed in Step 7.). To generate these configurations, one coil must be pulled away from the other coil. The coil was pulled away over the course of 500 picoseconds, with snapshots of the configurations saved every 1 picosecond. This pulling can be visualized by the pulling animation in Figure 1.
Figure 1. Visualization of a coil from the coiled-coil being pulled away from the other.
As can be seen by the pulling simulation (Figure 1), there is no displacement for some time. This is related to the force on the imaginary spring building up until it is sufficient to overcome the strong energetic forces stabilizing the coils. Later in the simulation we can see a coil begin to be pulled apart from the other. This can also be graphically represented through force on the harmonic spring (Figure 2.)
Figure 2. Quantification of the pulling force required to separate coiled-coils.
As can be seen in Figure 2., there is an initial peak in force on the harmonic spring (pull force) at about 100 picoseconds – representing the amount of force required to separate the coiled-coils. However, it is important to note that this is not representative of the actual binding energy (ΔGbind) of the coils.
Figure 3. Weighted Histogram Analysis Method (WHAM) to Determine Binding Energy.
As can be seen above, the PMF stabilizes at around 15 kcal mol-1, corresponding to a ΔGbind of about 15 kcal mol-1. This correlates with the published in vitro ΔGbind (11.3 kcal mol-1) value for similarly designed coils(1), suggesting that our coils were designed successfully and are stable.
Although our in silico results aligned with the published in vitro value for coiled-coil relatively closely, there were some noticeable artifacts in the generation of our PMF figure. Namely, the artifacts present at about ξ = 1.0, ξ = 1.6, and ξ = 1.9. These artifacts reflect a lack of sampling, as can be corroborated by the histograms underneath. As no umbrella sampling window was centered around these high-energy states the sampling conducted there was insufficient. Therefore, additional steps will be carried out in the final stages of umbrella sampling to eliminate any artifacts and ensure accuracy.
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