Probing designability via a generalized model of helical bundle geometry.

Area of Science:

• Structural biology
• Computational biology
• Protein design

Background:

• Protein structures exhibit degeneracy with recurring motifs, necessitating methods to represent them using collective, physically relevant coordinates.
• Understanding the space of designable protein structures is crucial for de novo protein design, aiming to stabilize conformations with numerous sequences.

Purpose of the Study:

• To delineate the space of designable protein structures by parameterizing geometric diversity.
• To apply and validate a parameterization framework, initially the Crick parameterization, to alpha-helical coiled coils and subsequently to generalized helical structures.

Main Methods:

• Utilized the Crick parameterization to analyze the geometric space of natural alpha-helical coiled coils.
• Developed a general mathematical framework for parameterizing arbitrary helical structures, applicable to non-coiled-coil helical bundles.
• Validated the framework on helical bundles found in channels and transporter proteins.

Main Results:

• Over 95% of known coiled-coil structures fit within a 1-Å C(α) root mean square deviation of a Crick-ideal backbone.
• Natural coiled-coil geometry is restricted, characterized by specific axial offsets, superhelical radii, amino acid propensities, and rotational angles.
• The space of designable coiled-coil structures is estimated to be at least 160-fold smaller than geometrically feasible structures.
• The generalized framework successfully parameterized helical bundles exhibiting helix bending.

Conclusions:

• Protein structure parameterization significantly reduces the search space for de novo protein design.
• The developed framework provides a generalizable method for analyzing and designing helical protein structures.
• Available web tools and code facilitate the application of these parameterization methods.