J Solution Chem (2010) 39: 943–958 DOI 10.1007/s10953-010-9556-3 Topological Quantities Determining the Folding/Unfolding Rate of Two-state Folding Proteins Jaewoon Jung · Alan J. Buglass · Eok-Kyun Lee Received: 6 November 2009 / Accepted: 3 February 2010 / Published online: 9 July 2010 © Springer Science+Business Media, LLC 2010 Abstract We investigate various topological and energy parameters from the protein native structure and find combinations of some parameters that are well correlated with the rate of folding/unfolding. For folding, the topological quantity that combines the clustering coeffi- cient and the long-range order (or total contact distance/contact order) has a high correlation with the folding rate, expressed as ln k F , obtained from standard experimental conditions. For unfolding, a combination of the impact of edge removal, obtained from the protein struc- ture, and the stability of the native protein structure, as expressed by the free energy change G, gives a good correlation with unfolding rate, ln k U . Keywords Protein folding · Contact order · Long-range order · Total contact distance · Clustering coefficient · Impact of edge removal 1 Introduction Recently, there have been growing efforts to investigate the folding and unfolding kinetics of proteins by experimental and theoretical means [1–27]. In particular, there is now much experimental data to indicate that those proteins undergoing a two-state folding/unfolding mechanism share common properties, and consequently the mechanism for this has been and is an active issue in the protein folding problem because of its simplicity as well as its prevalence [3–17]. Progress has been achieved by Plaxco and Baker [18, 19], who have defined a topological quantity named relative contact order and have shown that this quantity has a strong correlation with the folding rates of two-state folding proteins. After their work, various quantities having similar properties to the relative contact order have been suggested, J. Jung ( ) Graduate School of System Informatics, Kobe University, Nada-ku, Kobe 657-8501, Japan e-mail: jwjung@gold.kobe-u.ac.jp A.J. Buglass · E.-K. Lee Department of Chemistry, Korea Advanced Institute of Science and Technology, Yusong-gu, Daejeon 351-701, Korea