(Tue, 02/16/2021 - 19:50 | 5 comments)
Can you display derivatives or gradients of Electron Density clouds in Foldit?
|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: https://en.wikipedia.org/wiki/Gradient 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: http://www.sci.utah.edu/~gerig/CS7960-S2010/handouts/04%20Gaussian%20derivatives.pdf shows 0th to 7th derivatives of Gaussians in Fig 4.1 on p.54. https://cedar.buffalo.edu/~srihari/CSE555/Normal2.pdf shows 0th to 3rd derivatives of Gaussians in Fig A.2 on p.1.