I was asked to use MD simulation to measure the spring constant of a polymer chain. I didn't find any references about this. It seems that people use AFM to do this.
I plan to run ordinary MD simulation with AMBER to make the polymer from linear initial structure to a globular conformation. Then extract several conformations with different radius of gyration and corresponding potential energies or calculate the potential using Gaussian with STO-3G. I don't know whether the data would be a parabola.
Do you have any idea about this?
You can employ steered molecular dynamics in one form or another. You can restrain the end-to-end distance of the chain and measure the restraint force, from which you can calculate the force constant. This gives you better sampling of extended conformations and I would expect the values to converge faster with this setup.
I work with gomacs and not amber, but I am sure the method is transferable.
You will almost certainly not get a parabola. In fact, you can't find a single spring or rubber band in existence that gives a parabolic potential as a function of extension or compression -- there are always anharmonic effects that get larger the further you get from the 'relaxed' state.
The force constants are derived by taking the coefficient of the coefficient of the 2nd-order term in the Taylor series expansion for your potential energy function about your 'equilibrium' distance.
That said, Erik's suggestions are good -- you will likely get farther with a PMF-based method like steered MD or umbrella sampling. You can use end-to-end distance like he suggested (simplest), or use the radius of gyration as a collective variable to sample along that coordinate.
Thanks!
Extending the polymer in 10ns in vacuum. I got the following figure.
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