Can you display derivatives or gradients of Electron Density clouds in Foldit?

Case number:845833-2011209
Topic:Game: Display
Opened by:jeff101
Opened on:Tuesday, February 16, 2021 - 19:50
Last modified:Wednesday, February 17, 2021 - 22:35

In Foldit's Electron Density Puzzles, sometimes
it is hard to see certain features of the ED cloud.
I assume the ED cloud is just a 3D plot of a scalar
function f(x,y,z), where f is the electron density
at the point x,y,z in cartesian coordinates. 
I assume that f is like a sum of Gaussians with
each Gaussian centered on a particular atom in
the protein. I wonder if it would be easier to
see certain features in f if the gradient of f 
was displayed instead. The gradient of f is a 
vector defined as grad f = (df/dx, df/dy, df/dz).
Usually such vectors are displayed as arrows that
point from low density f to high density f, but one 
could plot the magnitude of grad f instead to give 
a scalar, and then you could use the same display 
methods used in Foldit for the scalar quantity f.

For more details on the gradient, see:

Electron Spin Resonance (ESR) and Electron 
Paramagnetic Resonance (EPR) spectra often use 
derivatives of Gaussians (or Lorentzians) to reveal 
features. The most common spectra are displayed as 
1st derivatives, but 0th derivative (absorption) 
and 2nd derivative spectra are also sometimes used. 
One problem with higher derivatives is that they 
amplify any noise in the spectra, so some features 
become hidden by the noise. Higher derivative 
spectra also look more complicated than lower
derivative ones.

Below are some links showing Gaussians and their
first few derivatives:
shows 0th to 7th derivatives of Gaussians in Fig 4.1 on p.54.
shows 0th to 3rd derivatives of Gaussians in Fig A.2 on p.1.

(Tue, 02/16/2021 - 19:50  |  5 comments)

jeff101's picture
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Matlab's website describes several edge detection methods 
that seem to use the magnitude of the gradient:

Below gives more general information about edge detection 
(including some pictures):
jeff101's picture
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You could keep Foldit's Electron Density menu
the same, but add one or more sliders to pick 
which derivative (0th or 1st) of the density to 
display or which edge detection method to use.
horowsah's picture
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This is a good question- typically in crystallography-expert use software this sort of information is displayed with a second map that the user can choose to show that will display areas in which the protein model and the primary map disagree. It can actually be calculated in such a way as to provide a relatively unbiased appraisal of where the user needs to work the most. As of now, we can't do this in Foldit, but it is on the list of improvements we want to add.

jeff101's picture
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What you suggest, showing the difference between a model's 
calculated density and the actual experimental density,
would certainly be helpful. It would also be helpful if 
we could display our latest solution's calculated density. 
Right now, Foldit just shows the experimental density. The
closest Foldit comes to showing the calculated density is 
if you select "Sphere, Show All H, and Show All Sidechains" 
or "Show isosurface" in the View Menu.

What most of my Feedback above suggests is showing the
gradient or derivatives of the experimental density. 
Showing the derivative of an experimental density puts 
more emphasis on edges in the density (points where the 
density is changing quickly). Showing the derivative 
also gives zeroes in ranges of constant density, peak
density, and minimum density. The derivatives and 
gradient of the experimental density are largest in
magnitude at the edges of the experimental density.

jeff101's picture
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Somewhat related to your response is a potential 
scoring problem that may have occurred in Puzzle 
1952 as well as other previous ED Puzzles:

Since ED puzzles have more than one ED cloud
(a visible one and a periodic lattice of invisible 
ones extending in all directions), it is possible
to have a solution with, for example, segments 1-10
in one ED cloud and segments 145-154 in another ED
cloud. It might even be possible for segments 1-10
to settle into the same part of the ED cloud that 
segments 145-154 settle into. If they were in just
one ED cloud instead of straddling 2 ED clouds,
these segments would be overlapping and clashing,
and the score would reflect this. Nevertheless,
because each segment range is in a different ED 
cloud, there is no clashing contribution to the 
overall score, and the score won't make sense.

It might help to imagine breaking all of space
into a bunch of identical boxes, one box for 
each ED cloud. If one then shifts the contents 
of all of these boxes into the box containing 
the visible ED cloud, all their ED clouds would 
overlap. If the protein began entirely within 
one ED cloud, the protein would remain intact
and end up in the visible ED cloud. Nevertheless,
if the protein straddled more than one ED cloud,
the protein would get chopped into pieces, one
for each ED cloud it straddled, and some of 
these pieces might overlap with each other once
shifted into the box containing the visible
ED cloud. Overlapping protein pieces should
give a clashing penalty and drop the score.

Developed by: UW Center for Game Science, UW Institute for Protein Design, Northeastern University, Vanderbilt University Meiler Lab, UC Davis
Supported by: DARPA, NSF, NIH, HHMI, Amazon, Microsoft, Adobe, Boehringer Ingelheim, RosettaCommons