<pre>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.</pre></code>
Matlab's website describes several edge detection methods
that seem to use the magnitude of the gradient:
https://www.mathworks.com/help/images/ref/edge.html#buo5g3w-6
https://www.mathworks.com/help/images/ref/edge.html#buo5g3w-3
Below gives more general information about edge detection
(including some pictures):
https://www.mathworks.com/discovery/edge-detection.html
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.
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.
<pre>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.</pre></code>
Somewhat related to your response is a potential
scoring problem that may have occurred in Puzzle
1952 as well as other previous ED Puzzles:
https://fold.it/portal/node/2011169#comment-44009
https://fold.it/portal/node/2011169#comment-44033
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.
