## Helical indexing (layer-lines)

You may find this part difficult to learn. That's fine, everyone feels the same at the beginning.
Plus, there may be five people fully understanding this in the world. You could be the sixth.

Finish those readings before you look at FAQs.

## 1988-Stewart

Computer Image Processing of Electron Micrographs of Biological Structures with Helical Symmetry

A good start to understand power spectrum

## 2005-DeRosier

A tutorial on helical structures

Some examples given by David

## 2014-Egelman

Ambiguities in helical reconstruction

Understand power spectrum in 3D

## 2020-Egelman&Wang

cryo-EM of helical polymers

Some concepts and common pitfalls

## Let's walk through those questions

### What is a power spectrum?

The power spectrum of a time series describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum.

### How should the power spectrum be generated  (for estimating possible helical symmetries)

It has to be generated from raw particles (aligned), and then added together as an average power spectrum.

Why not generate from 2D averages? Two reasons:
(1) Some 2D averages are artifacts
(2) 2D classes are often sorted based on "out-of-plane" tilt, which will could give misleading information in the power spectrum

### Can you determine the helical symmetry from the power spectrum

No. It only gives you a list of possible helical symmetries. Sometime one is lucky to only have one possibility, but most of time, the number of possibilities ranges from 2 to 400

### The KEY equation?

Bessel order (function maximum, see the table) = 2πRr

R comes from the center of the layer-line (unit, Å-1)
r  is the radius (in the filament) where this signal comes from (between rmin and rmax, apparently)

#### What we do

Use cryo-EM to understand and design large assemblies