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Bioinformatics Advance Access published online on November 15, 2005
Bioinformatics, doi:10.1093/bioinformatics/bti775
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© The Author (2005). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received September 26, 2005
Revised November 9, 2005
Accepted November 9, 2005

Article

Mean curvature as a major determinant of {beta}-sheet propensity

Eunhee Koh 1 *, Taehyo Kim 2, and Hyun-soo Cho 3

1 Department of Biology, Yonsei University, 134, Sinchon-dong, Seodaemun-gu, Seoul, 120-749, Korea
2 POSCO, Technical Research Laboratories, 699, Gumho-dong, Gwangyang-si, Jeonnam, 545-090, Korea
3 Department of Biology, Yonsei University, 134, Sinchon-dong, Seodaemun-gu, Seoul, 120-749, Korea; Protein Network Research Center, Yonsei University, 134, Sinchon-dong, Seodaemun-gu, Seoul, 120-749, Korea

* To whom correspondence should be addressed.
Eunhee Koh, E-mail: ehkoh{at}yonsei.ac.kr


  Abstract

Motivation: Despite the importance of {beta}-sheets as building blocks in proteins and also toxic elements in the pathological disorders, ranging from Alzheimer's disease to mad cow disease, the principles underlying their stability are not well understood. Non-random {beta}-sheet propensities of amino acids has been revealed both by their distinct statistical preferences within known protein structures and by the relative thermodynamic scales through the experimental host-guest systems. However, the recent fitting analysis proved that a native {beta}-sheet conforms to a minimal surface with zero mean curvature, like the physical model of soap films.

Results: We here suggest that the stability of a residue in the all {beta}-sheet proteins can be measured with its mean curvature parameter, using the discrete differential geometry. The sharply decreasing mean curvature with increasing number of {beta}-strand identifies a significant cooperative effect whereby the interstrand interaction increases in strength with the number of {beta}-strands. Furthermore, strong correlations of mean curvatures with the previous {beta}-sheet propensities of amino acids show that their intrinsic differences in adopting the ideal {beta}-sheet structure are affected by the water-accessible area of side-chains, and result in the distinct statistical and thermodynamic {beta}-sheet propensities. Therefore, we conclude that mean curvature should be considered as the significant stability index of a {beta}-sheet structure.


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