PoissonBoltzmann Molecular Dynamics: Theory and Algorithms. Ray Luo Molecular Biology and Biochemistry University of California, Irvine. Different levels of abstraction: Approximations of biomolecules. Quantum description: electronic & covalent structure
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Ray Luo
Molecular Biology and Biochemistry
University of California, Irvine
Intermolecular Forces, A.J. Stone
Bonded
Potential
Energy
Electrostatic
Nonbonded
Repulsiondispersion
Multiple trajectories, often as many as 10s to 100s, are needed
ru: solute coordinates; rv: solvent coordinates
Dielectric
constant
Charge density

ep
Charge of salt ion in solution
+


Electrostatic potential
+
+
+

s
Wrep: Estimated with surface (SES/SAS) or volume (SEV/SAV)
Watt: Approximated by (D. Chandler and R. Levy)
ε= 80
Linearized PoissonBoltzmann Equation:
where
Correlation Coefficient:
0.99995
Root Mean Square Deviation:
0.33 kcal/mol
AMBER/TIP3P Error (wrt Expt):
1.06 kcal/mol
AMBER/PB Error (wrt Expt):
0.97 kcal/mol
(neutral side chain analogs)
Tan et al, JPCB, 110, 1868018687, 2006
Tan and Luo, In Prep.
Tan and Luo, In Prep
Tan et al, JPCB, 111, 1226312274, 2007
Tan et al, JPCB, 111, 1226312274, 2007
CC: 0.9995
RMSD: 0.16kcal/mol
RMS Rel Dev: 0.01
Tan et al, JPCB, 111, 1226312274, 2007
Error bars too small to be seen
Tan and Luo, In Prep.
CC: 0.983
RMSD: 0.29 kcal/mol
RMS Rel Dev: 0.035
Tan and Luo, In Prep.
Error bars too small to be seen
Tan and Luo, In Prep.
Behaviors of Two Estimators for biomoleculesTYR SideChain Conformations
SAS
SAV
Tan and Luo, In Prep.
Maple, Cao, et al., J Chem Theo Comp, 1:694, 2005.
Schnieders, Baker, et al., J Chem Phys, 126:124114, 2007.
Solute dielectric constant ε is optimized
P
Tan and Luo, J Chem Phys, 126:094103, 2007.
Tan, Wang, and Luo, J Phys Chem, 112:7675. 2008.
Yes
Convergence
No
Tan and Luo, J Chem Phys, 126:094103, 2007.
1) Optimization with HF/631G*
2) Single point with B3LYP/ccpVTZ
monomers dimers
Left: 12 monomers in three environments (vacuum, ε = 4, water)
Right: 4 dimers in three environments
atomic radii: UA0 probe radius:1.385Å
Dipole moments of monomer with charges fitted simultaneously in three environments
Unit: Debye
rmsd: 0.2799 uavg: 0.2413 correlation: 0.9922
charges fitted simultaneously for both alphaL and c7eq
in three environments
 Large error in potential near singular charges
 Large error in dielectric boundary force
 Self energy between redistributed charges
Cai, Q. et al. Journal of Chemical Physics. 2009, 130, 145101.
inside
outside
On the dielectric boundary
Cai, Q. et al. Journal of Chemical Physics. 2009, 130, 145101.
 The potential is continuous on the interface
 Integrating the PBE and then using the Gauss’s law give the flux condition
Davis and McCammon, Journal of Computational Chemistry. 1991, 12, 909.
LeVeque and Li. SIAM Journal Numerical Analysis. 1994, 31, 1019.
Tested in the Poisson equation:
single particle system, dielectric boundary force
Wang, J. et al. Chemical Physics Letters. 2009, 468, 112.
Dielectric boundary force: Theory biomolecules
Dielectric boundary force: Theory biomolecules
Davis and McCammon, Journal of Computational Chemistry. 1990. 11. 401.
Xiang et al, Journal of Chemical Physics. 2009. submitted.
Dielectric boundary force: biomoleculesNewton’s third law
Xiang et al, Journal of Chemical Physics. 2009. submitted.
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NIH/GMS