### Parametric disasters

~ published by Brian Weitzner (original post from 09/03/2018) ~

I recently got a new computer and I have been (slowly) going through my old files to try to maintain a little order around here. So, while I was doing the ol’ twenty-first century upkeep, I stumbled across a file called “nope_nope_nope.mov”. Here’s what was in that file:

There’s another one called “strand_fail.mov” that looks like this:

What each of these movies show is a failed initial attempt at extending the parametric bundle design methods used in Rosetta. A little while ago, Vikram Mulligan and I sat down to think about what would be needed to describe a β barrel. We started off noting that a strand could be thought of as a helix in which every residue flips 180º, and that we would need to describe a “squishing” parameter to describe non-circular barrel systems.

I recently got a new computer and I have been (slowly) going through my old files to try to maintain a little order around here. So, while I was doing the ol’ twenty-first century upkeep, I stumbled across a file called “nope_nope_nope.mov”. Here’s what was in that file:

There’s another one called “strand_fail.mov” that looks like this:

What each of these movies show is a failed initial attempt at extending the parametric bundle design methods used in Rosetta. A little while ago, Vikram Mulligan and I sat down to think about what would be needed to describe a β barrel. We started off noting that a strand could be thought of as a helix in which every residue flips 180º, and that we would need to describe a “squishing” parameter to describe non-circular barrel systems.

Vikram recently moved on to the Flatiron Institute in New York, but this was a fun little project that kind of went nowhere so I thought I would share it here. Also, he took really detailed notes and made a lot of pretty pictures and it would be a shame for the world to not have them.

## First, some background

We have had some success designing helical bundles from parametric equations first developed by Francis Crick. These equations enable us to calculate the coordinates of each helical residue’s α carbon using descriptors with clear physical meanings, which allows us to specify geometric properties or requirements of a helical bundle and quickly trace out a backbone based on those requirements.

The equations are:

Grigoryan and DeGrado described the parameters as:

- Superhelical radius,
- Superhelical frequency/twist,
- Superhelical phase,
- Helical radius,
- Helical frequency/twist,
- Helical phase,
- Offset along the axis,
- Pitch angle, , where is the distance between residues
- Superhelical phase (decoupled from the offset),

Calculations are made a little simpler by holding and fixed at the values for ideal helices (1.51 and 2.26 Å), and by distributing helices evenly about the axis, which gives legal values of

## How can we incorporate a “squish”?

One of the simplifying assumptions that is used in the equations above is that all parameters are constants. But when we want to model barrels with non-circular cross sections, that simplification leaves the room. In this case, the superhelical radius will depend on a new parameter, , the eccentricity of the elipse. Here’s a photo of a white board where we derived this:

With the new term, we can stretch barrels in one dimension and evaluate metrics like hydrogen bonding along the way:

Here’s what it looks like normal to the barrel axis:

And then, finally, one can generate parameters and use some metric to perform monte carlo sampling of a parametrically-designed β barrel.

Thanks for all the fun times and good work, Vikram!

## Comments

## Post a Comment