# How does the length of separation between stacks in multiloops and hooked or open-loops affect the free energy of the loop?

I noticed a behavior today that I did not expect while trying to solve a puzzle. I have tried to illustrate it in the image below:

Does anyone know if this is always the case, and what variations there are on this? I know adjacent stacks (separated by zero number of bases) also affect the loop energies but I have not looked into it at all, and maybe it is already addressed in someone’s guide somewhere.

Also, it seems like stacks that are separated by more than two bases in these multiloops or hook loops will not have a different combined energy effect on the loops based on their closing pairs. And since it appears that multi loops and hook loops do not automatically increase in energy as their size increases (as other loops do with only a couple of specific exceptions) I am thinking maybe these narrowly separate stacks’ energy influences are sort of a special case worth exploring

If this question is too confusing just say so and I’ll put up more images (unless I change my mind or become lazy)

The difference in energy is EteRNA’s attempt to model the energy contribution of coaxial stacking. - the idea is that adjacent stacks will align along a common axis in the 3d structure of the RNA. The NNDB website has examples of energy calculations for this sort of thing, but they’re confusing and seem inconsistent with the values displayed in EteRNA.

As far as puzzle design is concerned, here is what I’ve observed:

• Energy is higher than stacks separated by >1 nt, but lower than energy for stacks with no separation

• GC pairs always stabilize the adjoining multiloop/external loop more than AU pairs

• The orientation of base pairs in all stacks influences multiloop/external loop energy

• If an AU/GU pair closes the 5’-most stack, it destabilizes the multiloop/external loop less than the same closing pair in a different stack

For stacks separated by 0 nt:

<- Energy is higher than when both stacks are separated by 1 nt

• GC pairs always stabilize the adjoining multiloop/external loop more than AU pairs

• If an AU/GU pair closes the 5’-most stack, it destabilizes the multiloop/external loop less than the same closing pair in a different stack

• If 3 or more stacks are separated by 0 nt, the orientation of base pairs in the middle stack(s) does not influence loop energy

The difference in energy is EteRNA’s attempt to model the energy contribution of coaxial stacking. - the idea is that adjacent stacks will align along a common axis in the 3d structure of the RNA. The NNDB website has examples of energy calculations for this sort of thing, but they’re confusing and seem inconsistent with the values displayed in EteRNA.

As far as puzzle design is concerned, here is what I’ve observed:

• Energy is higher than stacks separated by >1 nt, but lower than energy for stacks with no separation

• GC pairs always stabilize the adjoining multiloop/external loop more than AU pairs

• The orientation of base pairs in all stacks influences multiloop/external loop energy

• If an AU/GU pair closes the 5’-most stack, it destabilizes the multiloop/external loop less than the same closing pair in a different stack

For stacks separated by 0 nt:

<- Energy is higher than when both stacks are separated by 1 nt

• GC pairs always stabilize the adjoining multiloop/external loop more than AU pairs

• If an AU/GU pair closes the 5’-most stack, it destabilizes the multiloop/external loop less than the same closing pair in a different stack

• If 3 or more stacks are separated by 0 nt, the orientation of base pairs in the middle stack(s) does not influence loop energy