Relating time complexity of protein folding simulation to approximations of folding time

Steinhofel, K., Skaliotis, A. and Albrecht, Andreas A. (2007) Relating time complexity of protein folding simulation to approximations of folding time. Computer Physics Communications, 176 (7) . pp. 465-470. ISSN 0010-4655 [Article] (doi:10.1016/j.cpc.2006.12.002)

Abstract

Finkelstein and Badretdinov [A.V. Finkelstein, A.Y. Badretdinov, Rate of protein folding near the point of thermodynamic equilibrium between the coil and the most stable chain fold, Fold. Des. 2 (1997) 115–121] approximated the folding time of protein sequences of length n by exp(λ⋅n2/3±χ⋅n1/2/2)ns, where λ and χ are constants close to unity. Recently, Fu and Wang [B. Fu, W. Wang, A 2O(n1−1/d⋅logn) time algorithm for d-dimensional protein folding in the HP-model, in: J. Daz, J. Karhumäki, A. Lepistö, D. Sannella (Eds.), Proceedings of the 31st International Colloquium on Automata, Languages and Programming, in: Lecture Notes in Comput. Sci., vol. 3142, Springer-Verlag, Heidelberg, 2004, pp. 630–644] published an exp(O(n1−1/d)⋅lnn) algorithm for d-dimensional protein folding simulation in the HP-model, which is close to the folding time approximation by Finkelstein and Badretdinov and can be seen as a justification of the HP-model for investigating general complexity issues of protein folding. We propose a stochastic local search procedure that is based on logarithmic simulated annealing. We obtain that after (m/δ)a⋅D Markov chain transitions the probability to be in a minimum energy conformation is at least 1−δ, where m⩽b(d)⋅n is the maximum neighbourhood size (b(d) small integer), a is a small constant, and D is the maximum value of the minimum escape height from local minima of the underlying energy landscape. We note that the time bound is instance-specific, and we conjecture D<n1−1/d as a worst case upper bound. We analyse View the MathML source experimentally on selected benchmark problems for the d=2 case.

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