Coordinate-dependent diffusion in protein folding

被引:241
作者
Best, Robert B. [1 ]
Hummer, Gerhard [2 ]
机构
[1] Univ Cambridge, Dept Chem, Cambridge CB2 1EW, England
[2] NIDDK, Chem Phys Lab, NIH, Bethesda, MD 20892 USA
基金
美国国家卫生研究院;
关键词
coordinate transformation; internal friction; kinetic prefactor; projected dynamics; reaction coordinate; UNFOLDED POLYPEPTIDE-CHAINS; BETA-HAIRPIN FORMATION; SPEED LIMIT; ENERGY LANDSCAPE; INTERNAL-FRICTION; TRANSITION-STATES; SOLVENT VISCOSITY; CONTACT FORMATION; 3-HELIX BUNDLE; LOOP FORMATION;
D O I
10.1073/pnas.0910390107
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Diffusion on a low-dimensional free-energy surface is a remarkably successful model for the folding dynamics of small single-domain proteins. Complicating the interpretation of both simulations and experiments is the expectation that the effective diffusion coefficient D will in general depend on the position along the folding coordinate, and this dependence may vary for different coordinates. Here we explore the position dependence of D, its connection to protein internal friction, and the consequences for the interpretation of single-molecule experiments. We find a large decrease in D from unfolded to folded, for reaction coordinates that directly measure fluctuations in Cartesian configuration space, including those probed in single-molecule experiments. In contrast, D is almost independent of Q, the fraction of native amino acid contacts: Near the folded state, small fluctuations in position cause large fluctuations in Q, and vice versa for the unfolded state. In general, position-dependent free energies and diffusion coefficients for any two good reaction coordinates that separate reactant, product, and transition states, are related by a simple transformation, as we demonstrate. With this transformation, we obtain reaction coordinates with position-invariant D. The corresponding free-energy surfaces allow us to justify the assumptions used in estimating the speed limit for protein folding from experimental measurements of the reconfiguration time in the unfolded state, and also reveal intermediates hidden in the original free-energy projection. Lastly, we comment on the design of future single-molecule experiments that probe the position dependence of D directly.
引用
收藏
页码:1088 / 1093
页数:6
相关论文
共 66 条
[1]   THE ROLE OF SOLVENT VISCOSITY IN THE DYNAMICS OF PROTEIN CONFORMATIONAL-CHANGES [J].
ANSARI, A ;
JONES, CM ;
HENRY, ER ;
HOFRICHTER, J ;
EATON, WA .
SCIENCE, 1992, 256 (5065) :1796-1798
[2]   Reaction coordinates and rates from transition paths [J].
Best, RB ;
Hummer, G .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2005, 102 (19) :6732-6737
[3]   Diffusive model of protein folding dynamics with Kramers turnover in rate [J].
Best, RB ;
Hummer, G .
PHYSICAL REVIEW LETTERS, 2006, 96 (22)
[4]   Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules [J].
Best, Robert B. ;
Paci, Emanuele ;
Hummer, Gerhard ;
Dudko, Olga K. .
JOURNAL OF PHYSICAL CHEMISTRY B, 2008, 112 (19) :5968-5976
[5]   Protein folding kinetics under force from molecular simulation [J].
Best, Robert B. ;
Hummer, Gerhard .
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 2008, 130 (12) :3706-+
[6]   The speed limit for protein folding measured by triplet-triplet energy transfer [J].
Bieri, O ;
Wirz, J ;
Hellrung, B ;
Schutkowski, M ;
Drewello, M ;
Kiefhaber, T .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1999, 96 (17) :9597-9601
[7]   CHARMM: The Biomolecular Simulation Program [J].
Brooks, B. R. ;
Brooks, C. L., III ;
Mackerell, A. D., Jr. ;
Nilsson, L. ;
Petrella, R. J. ;
Roux, B. ;
Won, Y. ;
Archontis, G. ;
Bartels, C. ;
Boresch, S. ;
Caflisch, A. ;
Caves, L. ;
Cui, Q. ;
Dinner, A. R. ;
Feig, M. ;
Fischer, S. ;
Gao, J. ;
Hodoscek, M. ;
Im, W. ;
Kuczera, K. ;
Lazaridis, T. ;
Ma, J. ;
Ovchinnikov, V. ;
Paci, E. ;
Pastor, R. W. ;
Post, C. B. ;
Pu, J. Z. ;
Schaefer, M. ;
Tidor, B. ;
Venable, R. M. ;
Woodcock, H. L. ;
Wu, X. ;
Yang, W. ;
York, D. M. ;
Karplus, M. .
JOURNAL OF COMPUTATIONAL CHEMISTRY, 2009, 30 (10) :1545-1614
[8]   Exact solution of the Munoz-Eaton model for protein folding [J].
Bruscolini, P ;
Pelizzola, A .
PHYSICAL REVIEW LETTERS, 2002, 88 (25) :4
[9]   INTERMEDIATES AND BARRIER CROSSING IN A RANDOM ENERGY-MODEL (WITH APPLICATIONS TO PROTEIN FOLDING) [J].
BRYNGELSON, JD ;
WOLYNES, PG .
JOURNAL OF PHYSICAL CHEMISTRY, 1989, 93 (19) :6902-6915
[10]  
Buscaglia M, 2006, BIOPHYS J, V91, P276, DOI [10.1529/biophysj.105.071167, 10.1529/biophysj.105.0711667]