worm-like chain torsion

[Yan Zhang]

What is the best way to add a torsion rigidity to a worm-like chain in openmm? Specifically, I have a chain of beads connected by harmonic bond, and I want to restrict the rotation of the bonds. One way I can think of is add "side chains" to each of the beads, so that the torsional force field can be defined on the dihedral formed by two side chain beads and two backbone beads.

Yan

[Peter Eastman]

Are there any other constraints on the chain's mobility? If you add side chains and then apply torsions based on them, I'm not sure you're really doing anything more than restricting the motion of those side chains. Each torsion is independent of the configuration of the backbone. What unrestricted degrees of freedom do you want the backbone to have?

Peter

[Yan Zhang]

I want to simulate something like a rubberband, applying twisting to which will add up its torsional energy. Basically I want to see the following:

Untitled.png (23.27 KiB) Viewed 228 times

The left one is different from the right one because forcing the left one to become a circle will add up its torsional energy. If there is no torsional force field the two can convert to each other through thermal fluctuation.
I'm not sure if I explain myself clearly enough. Basically I want each bead on the chain to have some sort of orientation, based on which I can define the twisting of a fiber.

[Peter Eastman]

One way of modelling that would be to literally model it as a band with width. For each bead, have two particles side by side. They would be bonded to each other, and also to the next two particles down the chain. Something like this:

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Does that seem plausible?

[Maciej Jasiski]

Modeling as a band with width (and probably height also would be needed) is dramatically increasing number of degrees of freedom. While in mentioned case, we need only one additional degree: the torsional angle between two bits. It can be done by adding body fixed coordinate system for each bead. The theory behind that is described for example in these articles:

Chiroco, Langowski 1994
http://onlinelibrary.wiley.com/doi/10.1 ... 40313/epdf

Klein, Merlitz, Langowski 1998
http://ac.els-cdn.com/S0006349598740032 ... 4417ba057b

How can something like that be implemented in OpenMM?

[Peter Eastman]

It has exactly the same number of degrees of freedom as if you added the second particle as a sidechain and used a torsion, as you originally suggested. Either way you have two particles per bead. They only differ in the potential function. You could try both and see how they work.

The other option is to stick with only one particle per bead and use torsions defined by four successive beads. But to do that, you also need to apply angle potentials to keep any part of the chain from fully straightening out. If it does, the dihedral angle becomes undefined and the energy becomes singular.