Folding funnels and frustration in off-lattice minimalist protein landscapes
Abstract
A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.
Footnotes
-
↵ ‡ To whom reprint requests should be addressed. e-mail: jonuchic{at}ucsd.edu.
-
This paper was presented at the colloquium “Computational Biomolecular Science,” organized by Russel Doolittle, J. Andrew McCammon, and Peter G. Wolynes, held September 11–13, 1997, sponsored by the National Academy of Sciences at the Arnold and Mabel Beckman Center in Irvine, CA.
-
↵ § Refs. 1 and 71 provide a detailed description for this formalism, including the dependence of the glass transition on the order parameters.
-
↵ ¶ For both models, we work in reduced units—i.e., all units are defined in terms of the monomer mass M, the bond length σ, and the energy ɛ. Time is thus measured in units of τ = σ⋅
and friction in units of
τ−1. Also, all bonds are fixed with the shake algorithm
(75), and bond angles are set to have a rest value of 105° and a
spring constant of 40ɛ(rad)−2. The BPN model has stiff
local trans preferences for the dihedral angles except at
the loop regions. Thus the BPN coefficients for the dihedral
interactions are set as A = 1.2ɛ and B =
0.2ɛ for all the dihedral interactions except those involving
two or more neutral monomers, in which case, A = 0.0ɛ
and B = 0.2ɛ, leading to a small barrier but no
preference among the three possible backbone rotamers. As a consequence
of this choice of dihedral coefficients, rigid strands appear at all
temperatures below the collapse temperature.
-
↵ ‖ This model is also similar to the associative memory hamiltonian used by Wolynes and collaborators (48) in the limit of a single memory.
-
↵ ** The ruggedness for the Gō-like model is very small because the energy is roughly proportional to Q. This is apparent from Fig. 7, where the entropy as a function of Q is almost temperature independent.
- ABBREVIATIONS:
- MD,
- molecular dynamics;
- MFPT,
- mean first passage time;
- MODC,
- molecule optimal dynamic coordinates
- Copyright © 1998, The National Academy of Sciences
