Structure optimization of BLN protein models combining local-search, evolutionary, and genetic approaches

Establishing relations between the amino acid sequence of a protein and its spatial structure is a very important and challenging task.
When analysing the forces affecting the protein folding, the investigation of the related free energy landscape is of central importance.
Thereby, to obtain the ground state and low-energy metastable states, highly effcient structure optimization tools are needed.
Here, we study the properties of genetic local-search type optimization approaches, in particular of thermal cycling (TC) [1] and systematic-crossover localsearch (SCLS) algorithms.
For this aim, we focus on the BLN protein model, designed by J.D. Honeycutt and D. Thirumalai [2]. We consider 46-, 58-, and 69-bead sequences from Refs. [2,3]; the 69-bead sequence seems to be the largest BLN model treated in the liteature up to now.
In all these cases, the TC and SCLS algorithms reliably find the global minimum within reasonable computing times.
Both algorithms proved to be far more effcient than multi-start local-search and simulated annealing approaches.
In the present work, to the best of our knowledge, the BLN model with rigid bond lengths is studied in detail for the first time.
We compare our results to the properties of the extended model by Berry et al. [4], in which stiff spring-like bonds are substituted for the rigid bonds:
The hardening of the spring constants causes several level crossings of the metastable states.
For the 46-bead model, this concerns even the ground state.

[1] A. Möbius, A. Neklioudov, A. Diaz-Sanchez, K.H. Hoffmann, A. Fachat, and M. Schreiber, Phys. Rev. Lett. 79 (1997) 4297.
[2] J.D. Honeycutt and D. Thirumalai, Biopolymers 32 (1992) 695.
[3] M.T. Oakley, D.J.Wales, and R.L. Johnston, J. Phys. Chem. B 115 (2011) 11525.
[4] R.S. Berry, N. Elmaci, J.P. Rose, and B. Vekhter, Proc. Natl. Acad. Sci. USA 94 (1997) 9520.