Several problems in free energy calculation
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Transcript of Several problems in free energy calculation
Several problems in free energy calculation
Institute of Biophysics
Hebei University of Technology
JI Qing
河北工业大学 生物物理研究所
July 2013, Beijing
1. Free energy change for kinesin’s neck linker docking
R.Vale & R.Milligan, Science, 2000.
Force generation vs neck linker docking
Rice et al., Biophysical Journal, 2003
3 /G kJ mol
Method: EPR, spin marker
lnG RT K
K = mobile + intermediate probes
immobilized probes
Too small !
Hackney, PNAS, 2005
Free energy change for NL docking
ATP hydrolysis:
55 /G kJ mol
6 8
28.8 /
W pN nm
kJ mol
Work:
What’s the problem?
Rice et al., Nature, 1999
extra turn
0
0
9
CNBCover-neck-bundle (CNB) = 0 + neck linker (9)
Hwang et al., Structure, 2008
The problem arises from the understanding of the neck linker docking mechanism.
Neck linker (~ 14 AA) consists of three parts: extra turn, 9 and 10.
Neck linker docking consists of three steps:
(1) Extra turn formation,
(2) 9 docking,
(3) 10 docking.
2. System-environment interaction vs free energy calculation
Jarzynski’s equality (JE) : W Fe e Jarzynski, PRL, 1997
(1) Single-molecule measurement (2) Steered molecular dynamics simulation
Liphardt et al., Science, 2002 Park et al., JCP, 2003
in solution in vacuum
Weak coupling assumption ?
JE is valid for sufficiently weak coupling between the system and reservoir. Neglecting Hint
The fluctuations in the work W must not be much greater than kBT. This condition pretty much rules out macroscopic systems of interest.
1 (298.15 ) 2.4789 /Bk T K kJ mol
ATP hydrolysis: 55 /G kJ mol
6 8 28.8 /W pN nm kJ mol Work by kinesin :
H-bond energy: 20 /HE kJ mol
11.72 /F kJ mol
Je-Luen Li, Roberto Car, Chao Tang, and Ned S. Wingreen, PNAS, 2007
The free energy change for the hydrophobic binding of two methane molecules (CH4) in water :
Jarzynski, PRL, 1997
3. Water system: hydrogen bond identification
“r- ” criterion : 1.59 Å < rO…H < 2.27 Å, > 140°
Pan et al., JCP, 2012
Kuo et al., Science, 2007
Geometric criterion for H bond:
Electronic orbitals of water dimerF E T S
H-H radial distribution function for bulk water
Soper, Chem. Phys., 2000repulsion
E hydrogen bonds
Energy criterion for H bond: 10 /E kJ mol
Number of H bond
“r- ” criterion
Energy criterion
1000 water pairs
701
528
CPMD method, 64 water molecules
Summary
1. The understanding of the system operating mechanism might affect the experiment design and calculation of free energy.
2. When Hint is comparable with Hsystem, can I directly use Jarzynski’s equality?
3. Water is the most important environment in our world. Water molecule is one of the most important biomolecules. The statistical description of the macroscopic behavior of water must be based on the quantitative knowledge of the microscopic structure and interaction of water molecules. The quantitative calculation of the free energy of water system is still a difficult task.
Acknowledgement
吕 刚( Gang Lv)张 辉( Hui Zhang )张 博( Bo Zhang )张秀欣( Xiu-Xin Zhang )潘 章( Zhang Pan )耿轶钊( Yi-Zhao Geng )李 铁( Tie Li )覃静宇( Jing-Yu Qin )刘书霞( Shu-Xia Liu )柳睿殊( Rui-Shu Liu )
The National Natural Science Foundation of China , No. 90403007
The National Natural Science Foundation of China , No. 10975044
My students :卓益忠( Yin-Zhong Zhuo)
包景东( Jing-Dong Bao)
张红雨( Hong-Yu Zhang)
晏世伟( Shi-Wei Yan)
My friends and collaborators :