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고등과학원

Protein folding and global optimization

Jooyoung Lee

Korea Institute for Advanced Study

Introduction

Computation of  protein structure is one of the challenges of contemporary biology. A fundamental approach to this problem, using first principles, is based on the thermodynamic hypothesis formulated by Anfinsen [1]. The three-dimensional structure of a native protein in its physiological environment is the one in which the free energy of the whole system is lowest. Successful protein structure computation with this approach entails two separate and very difficult problems: deriving a reliable potential energy function and developing an efficient optimization method for conformational search.

Although the thermodynamic approach [2] is base on sound physical grounds, it has not been as successful as other approaches such as sequence-homology and threading methods. Two main obstacles are the insufficient quality of available force fileds and the multiple minima problem. Protein structure prediction based solely on the thermodynamic hypothesis has heretofore been considered to be infeasible [3]. In this report we present a novel approach for protein structure computation based on global optimization of a potential energy function, and demonstrate its feasibility in blind tests on CASP3 experiments [4].

Conformational Space Annealing

Recently, we developed a very efficient method of conformational search called the Conformational Space Annealing (CSA) method [5-7]. One of the greatest advantages of the CSA method is that it can find many families of low-energy conformations that have distinct backbone structures. This makes it possible to search the whole conformational space of proteins for given potential functions. Only after such a successful conformational search has been accomplished, can the global minimum-energy conformation (GMEC) of a given function be obtained. CSA has been tested on the Empirical Conformational Energy Program for Peptides and Proteins (ECEPP/3) force field [8]. It has found the GMEC of the pentapeptide [Met5]enkephalin in 36 seconds of wall clock time, using 16 processors of an IBM SP2 supercomputer; for the N-terminal 20-residue membrane-bound portion of melittin, it found conformations with lower energies than those computed so far by other methods [6,7]. Furthermore, it was found that there are at least five different familes of conformations, one of which (the second lowest-energy family) contained the conformation previously considered as the GMEC.

The success of the CSA method in conformational searches of polypeptides with the ECEPP/3 force field suggests that this method, when combined with the UNRES [9-11] force field, can make the conformational search of protein possible in real time. This will, in turn, allow us to improve the UNRES force field.

In this report, we first demonstrate the state of art performance of protein structure calculation by applying the CSA method to the UNRES force field. For this, we searched the conformational space of two helical proteins: the 10-55 fragment of the B domain of staphylococcal protein A whose structure was determined by NMR spectroscopy and apo calbindin D9K, a 75-residue calcium-binding protein, whose structure was determined by NMR spectroscopy (PDB code: 1CLB) [12].

CASP3 experiments

After the successful demonstration of our approach on proteins with known structures, we went further by applying the same procedure in blind structure prediction tests on CASP3 experiments [4]. The overall results from CASP3 were comparable to the benchmark results on protein A and apo calbidin. Comparison of the computed lowest-energy structures with the crystal structures, released by the PDB after the predictions were made, shows that 61-residue fragments of proteins were predicted with RMSD's of 4.2[eqn: ANGSTROM]and 6.0[eqn: ANGSTROM] for the [eqn: C^ alpha] atoms, for HDEA and MarA, respectively [13.14]. This demonstrates that protein structure can be predicted based solely on global optimization of a potential energy function for a given amino acid sequence.

The native structure of HDEA is a five-helix bundle with a long loop between the third (H-3) and the fourth (H-4) helix (see the figure below).

The RMSD between the crystal and our predicted structure 4.2 [eqn: ANGSTROM]for the [eqn: C^ alpha] atoms, when the structures are superposed from residues D25 to I85 (80% of the experimentally observed structure) which corresponds to native helices H-3, H-4, and H-5 (the first nine and the last four residues are missing in the crystal structure) Our model is different from the native structure in the packing of the 27-residue N-terminal part (residues 1 to 9 are not observed in the crystal structure). This N-terminal fragment, which contains H-2,

is rotated by approximately 180 degrees, resulting in an overall RMSD (residues 10 to 85) of 9.0[eqn: ANGSTROM]  for the [eqn: C^ alpha] atoms. Superposing helices H-2 and H-3 (residues W16 to K42), we obtain an RMSD for the [eqn: C^ alpha] atoms of 2.9 [eqn: ANGSTROM].

Parallel Computation

All our computations were performed by parallel computation using typically 64 CPUs. The parallel efficiency of our computation is estimated as 80 %, and details of the features of parallel computation using CSA can be found in ref. [15].

Conclusion

We demonstrated that with a powerful global search method such as CSA, protein structure can be predicted by global optimization of a potential energy function.

Top: Superposition of the crystal (red) and predicted (yellow) structures of HDEA. The[eqn: C^ alpha] atoms of the fragment included between residues D25 to I85 were superposed. The RMSD is 4.2[eqn: ANGSTROM]. Helices 3, 4 and 5 are indicated as H-3, H-4 and H-5, respectively.

Bottom: Superposition of the crystal (red) and predicted (yellow) structures of  the 27-residue fragment (W16 to K42) of HDEA. The [eqn: C^ alpha] atoms were superposed with an RMSD of 2.9 [eqn: ANGSTROM]. Helices 2 and 3 are indicated as H-2 and H-3, respectively.

References

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[3] Mirny, L. A. & Shakhnovich, E. I. (1998) J. Mol. Biol. 283, 507-526.

[4] Lee, J., Liwo, A., Ripoll, D.R., Pillardy, J. and Scheraga, H.A. (1999)

Proteins: Struc., Func., and Gen.,  Suppl. Vol. 3 204-208.

[5] Lee, J., Scheraga, H. A. & Rackovsky, S. (1997) J. Comput. Chem. 18, 1222-1232.

[6] Lee, J., Scheraga, H. A. & Rackovsky, S. (1998) Biopolymers 46, 103-115.

[7] Lee, J. & Scheraga H. A. (1999) Int. J. Quant. Chem. 75, 255-265.

[8] Nemethy, G., Gibson, K. D., Palmer, P. A., Yoon, C. N.,

Paterlini, G., Zagari, A., Rumsey, S. & Scheraga, H. A. (1992) J. Phys. Chem. 96, 6472-6484.

[9] Liwo, A., Oldziej, S., Pincus, M. R., Wawak, R. J., Rackovsky, S. & Scheraga, H. A. (1997) J. Comput. Chem. 18, 849-873.

[10] Liwo, A., Pincus, M. R., Wawak, R. J., Rackovsky, S., Oldziej, S. & Scheraga, H. A. (1997) J. Comput. Chem. 18, 874-887.

[11] Liwo, A., Kazmierkiewicz, R., Czaplewski, C., Groth, M., Oldziej, S.,

Wawak, R. J., Rackovsky S, Pincus, M. R. & Scheraga, H. A. (1998) J. Comput. Chem. 19, 259-276.

[12] Lee, J.; Liwo, A. and Scheraga, H.A. (1999) Proc. Natl. Acad. Sci. U. S. A. 96, 2025-2030.

[13] Liwo, A.; Lee, J.; Ripoll, D.R.; Pillardy, J. and Scheraga, H.A (.1999)

Proc. Natl. Acad. Sci., U. S. A. 96, 5482-5485.

[14] Lee, J.; Liwo, A.; Ripoll, D.R.; Pillardy, J.; Saunders, J.A.; Gibson, K.D.

and Scheraga, H.A. (2000) Int. J. Quant. Chem. 90-117.

[15] Lee, J.; Pillardy, J.; Czaplewski, C.; Arnautova, Y.; Ripoll, D.R.; Gibson,

K.D.; Wawak, R.J. and Scheraga, H.A. (2000) Comp. Phys. Comm. 128, 399-411.