The ruggedness of protein-protein energy landscape and the cutoff for 1/r^n potentials

The ruggedness of protein-protein energy landscape and the cutoff for 1/rn potentials

Anatoly M. Ruvinsky1 and Ilya A. Vakser2

1Anatoly M. Ruvinsky, Center for Bioinformatics, The University of Kansas, 2030 Becker Drive, Lawrence, Kansas 66047; tel: (785) 864-1057, fax: (785) 864-5558, email: ruvinsky@ku.edu 2Center for Bioinformatics and Department of Molecular Biosciences, The University of Kansas, Lawrence, Kansas 66047; 2030 Becker Drive, Lawrence, Kansas 66047; tel: (785) 864-1057, fax: (785) 864-5558, email: vakser@ku.edu

Keywords: docking, protein recognition, structure prediction, structural bioinformatics ABSTRACT The interaction cutoff contribution to the ruggedness of protein-protein energy landscape (the artificial ruggedness) is studied in terms of relative energy fluctuations for 1/rn potentials based on a simplistic model of a protein complex. Contradicting the principle of minimal frustration, the artificial ruggedness exists for short cutoffs and gradually disappears with the cutoff increase. The critical values of the cutoff were calculated for each of eleven popular power-type potentials with n=0÷9, 12 and for two thresholds of 5% and 10%. The artificial ruggedness decreases to tolerable thresholds for cutoffs longer than the critical ones. The results showed that for both thresholds the critical cutoff is a non-monotonic function of the potential power n. The functions reach the maximum at n=3÷4 and then decrease with the increase of the potential power. The difference between two cutoffs for 5% and 10% artificial ruggedness becomes negligible for potentials decreasing faster than1/ . The results suggest that cutoffs longer than critical ones can be recommended for protein-protein potentials. 12 r

2 INTRODUCTION Protein binding can be explained in terms of the funnel-based concept initially developed to describe protein folding 1-10. The concept suggests that unbound proteins are guided by the slope of the rugged energy landscape funnel into the bound state. The nature of the ruggedness and related effects is a subject of active research 11-14. Highly frustrated interactions are observed on the protein surface near the binding site 14. Mechanical unfolding experiments to measure the scale of the landscape ruggedness of proteins and RNAs have been suggested 15 and performed 16.
The amplitude of the of protein-protein energy landscape ruggedness has a component associated with the range of the energy potentials 12. The range of non-bonded inter-atomic interactions and related truncation methods are known to play an important role in protein folding 17-22, protein-protein docking 4,12, and all atom molecular dynamics and Monte-Carlo simulations of macromolecules and liquids 23-29. The cutoff is one of only two parameters used in coarse-grained normal mode analysis and elastic networks of proteins and their assemblies 30,31. The choice of the cutoff affects the functional form and performance of knowledge-based potentials in small molecule docking 32. The importance of long range interactions for protein stability 33, protein folding 34 and RNA binding 35 has been revealed experimentally.
The interactions are usually truncated at specific cutoff distances to reduce a number of interacting pairs of atoms or atomic groups in order to make feasible large scale macromolecular calculations. Despite the considerable progress achieved in methodology and computer power, the cutoff-related artifacts are still a bottleneck in macromolecular modeling. In comparison with other modeling approaches, the protein docking community has been less focused on the problem. Our attention to the cutoff problem is

3 motivated by observations that the choice of larger cutoffs results in the ruggedness depression 12 and thus in smooth protein-protein energy landscapes 4,36, which according with the principal of minimal frustration, 1,7,37 better approximate the actual binding landscape. Similar effects of the energy landscape smoothing due to the cutoff extension have been found in studies of liquids and atomic clusters 38-43, helix dimers 4,44,45 and protein complexes 4,36,46. We have recently demonstrated 12,47 that short cutoffs perturb protein-protein energy landscape and thus lead to false minima, changed positions and altered shape of true conformation-based minima. Such changes of the landscape impede the search for the global minimum in protein docking 4 and introduce errors in calculations of binding free energy 6,48-50. The false minima cause the artificial ruggedness of the energy landscape. The fine structure of the funnel or conformational substates 51 can be blurred due to the artificial ruggedness. The amplitude of the artificial ruggedness decreases with the increase of the cutoff 12. Thus it is important to know the cutoffs for different potentials that form a minimally frustrated funnel-like landscape, while al

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