Exploring the origins of topological frustration: Design of a minimally frustrated model of fragment B of protein A

Exploring the origins of topological frustration: Design of a minimally frustrated model of fragment B of protein A

^*Department of Molecular Biology, TPC6, The Scripps Research Institute, La Jolla, CA 92037; and ^†Department of Physics, University of California at San Diego, La Jolla, CA 92093

Edited by Harry B. Gray, California Institute of Technology, Pasadena, CA, and approved August 13, 1999 (received for review May 24, 1999)

Abstract

Topological frustration in an energetically unfrustrated off-lattice model of the helical protein fragment B of protein A from Staphylococcus aureus was investigated. This Gō-type model exhibited thermodynamic and kinetic signatures of a well-designed two-state folder with concurrent collapse and folding transitions and single exponential kinetics at the transition temperature. Topological frustration is determined in the absence of energetic frustration by the distribution of Fersht φ values. Topologically unfrustrated systems present a unimodal distribution sharply peaked at intermediate φ, whereas highly frustrated systems display a bimodal distribution peaked at low and high φ values. The distribution of φ values in protein A was determined both thermodynamically and kinetically. Both methods yielded a unimodal distribution centered at φ = 0.3 with tails extending to low and high φ values, indicating the presence of a small amount of topological frustration. The contacts with high φ values were located in the turn regions between helices I and II and II and III, intimating that these hairpins are in large part required in the transition state. Our results are in good agreement with all-atom simulations of protein A, as well as lattice simulations of a three- letter code 27-mer (which can be compared with a 60-residue helical protein). The relatively broad unimodal distribution of φ values obtained from the all-atom simulations and that from the minimalist model for the same native fold suggest that the structure of the transition state ensemble is determined mostly by the protein topology and not energetic frustration.

Footnotes

↵ ‡ To whom reprint requests may be addressed. E-mail: brooks{at}scripps.edu or jonuchic{at}ucsd.edu.
This paper was submitted directly (Track II) to the PNAS office.
↵ § These potentials were harmonic in the virtual dihedrals defined by four consecutive C_α atoms (beads).
Abbreviation:

PA,

protein A