Helical Capsid Pitch

Derive helical subunits per turn and axial pitch from measured rise and rotation.

Description

Convert a positive axial rise and rotation per subunit into subunits per turn and axial helical pitch.

A helical assembly relates successive repeating units through a translation along an axis and a rotation around that axis. The translation is the axial rise; the rotation is the twist. Pitch is the axial distance corresponding to one full 360-degree turn.^[1]

Dividing 360 degrees by the rotation gives the number of subunit steps per turn. That number can be fractional: a full turn need not end exactly on another discrete subunit. Multiplying it by the axial rise gives the pitch.

Helical Capsid Pitch applies that conversion to positive rise in angstroms and positive rotation in degrees. It reports magnitudes without identifying a structure, determining symmetry, or representing signed handedness.

When to translate helical rise and rotation into pitch

Use the tool when a compatible rise and rotation pair is already known for the same repeating unit. It is useful for checking units or comparing candidate geometric parameterizations.

Calculate subunit steps per complete turn.
Convert rise per subunit to axial pitch.
Retain noninteger turns rather than rounding to whole subunits.

How to enter helical parameters and calculate pitch

Enter positive Axial rise angstrom for one repeating subunit step.
Enter positive Rotation degrees per subunit no greater than 360; convert radians before entry.
Run the calculation and read Subunits per turn and Helical pitch angstrom.
Retain the repeating-unit convention and any independently established handedness with the result.

subunitsPerTurn = 360/rotationDegreesPerSubunit; helicalPitchAngstrom = axialRiseAngstrom×subunitsPerTurn

The implementation divides and multiplies directly, with no integer rounding or symmetry search. One angstrom equals 0.1 nanometer.

json

{
  "input": {
    "axialRiseAngstrom": 2,
    "rotationDegreesPerSubunit": 30
  },
  "output": {
    "subunitsPerTurn": 12,
    "helicalPitchAngstrom": 24
  }
}

Rotation 360° is allowed and gives one step per turn and pitch equal to rise. Zero or negative rise/rotation, rotation above one turn, and nonfinite inputs produce errors. Very small positive rotation can produce a large pitch.

Limitations and interpretation

Positive-only parameters do not encode left/right handedness or accept a negative twist directly.
The tool does not determine whether supplied parameters represent the true symmetry or smallest repeating unit.
No reconstruction, multi-start specification, radial geometry, physical capsid length, or structural validation is performed.
Subunits per turn is a geometric ratio, not the total number of subunits in a finite capsid.

Alternative or Complementary methods

Use a conventional icosahedral lattice count for a different symmetry model. A spherical-volume calculation requires a radius and answers a separate size question; pitch alone supplies no radius.

References

Helical symmetry in CryoSPARC — Structura Biotechnology; CryoSPARC Guide

Similar or alternative tools

Icosahedral Lattice Counts
Calculate conventional Caspar–Klug counts from lattice coordinates for an icosahedral architecture.
Sphere Volume Calculator
Calculate an ideal spherical volume from a supplied physical radius.