APM 530 - Lecture 6

32 Pages·2010·0.55 MB·English

by  Jay Taylor

ImplicitSolvationModels Overview
Solvation and Macromolecular Structure
The structure and dynamics of biological macromolecules are strongly
influenced by water:
Electrostatic effects: charges are screened by water molecules and
counterions.
Hydrophobic effect: Entropic forces favor conformations that
sequester non-polar hydrophobic domains within the interior of the
molecule.
Hydrodynamic effects: collision with solvent molecules imparts
kinetic energy to macromolecules.
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ImplicitSolvationModels Overview
Solvation of Nucleic Acids
Solvent effects on DNA and RNA are especially pronounced:
Screening of the negatively-charged phosphates by water and
counterions stabilizes helical and other tertiary structural motifs.
∼76% of the charge is reduced by water;
∼24% is reduced by divalent counterions.
The transition between A-form and B-form DNA is partly controlled
by hydration:
B-DNA has 18-30 waters per nucleotide.
A-DNA has 10-15 waters per nucleotide.
DNA bending is promoted by hydration of the phosphates.
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ImplicitSolvationModels Overview
DNA is surrounded by multiple layers of water.
Water density is increased up to six-fold in the first layer, especially
around the phosphates and in the minor and major groove.
A less stable second hydration shell extends out to 10˚A.
A spine of hydration runs through the minor groove.
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ImplicitSolvationModels Overview
Explicit Solvation Models
Solvent effects must also be included in molecular simulations. One
approach is to explicitly include a large number of solvent molecules
surrounding the macromolecule.
Boundary conditions are usually periodic.
Counterions can also be explicitly modeled.
A large number of solvent molecules is generally required:
Approximately 3000 waters are needed in a simulation of a 10 bp
DNA duplex.
Solvent viscosity leads to slower sampling of conformational space.
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ImplicitSolvationModels Overview
Implicit Solvation Models
Implicit solvent models represent the solvent and counterions as a
continuous medium.
Implicit simulations can usually be run more quickly than explicit
simulations.
We are usually not interested in the distribution of individual water
molecules in the solvent-solute interface.
Residence times of water in DNA vary from hundreds of picoseconds
to nanoseconds in the minor groove of A-tracts.
Several methods are available:
Solvent accessible surface area models
Poisson-Boltzmann equation
Generalized Born models
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ImplicitSolvationModels SASAmodels
Solvent Accessible Surface Area
SASA models express the free energy of solvation as a sum
(cid:88)
∆Gsolv = σ ASA
i i
i
where
the sum is over all atoms in the macromolecule;
ASA is the surface area of atom i accessible to the solvent;
i
σ is an atom-specific surface tension parameter.
i
The parameters σ have been estimated from empirical hydration free
i
energies for various organic compounds in water.
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ImplicitSolvationModels SASAmodels
Accessible Surface Area Calculations
Atoms and solvent molecules are both
modeled as spheres.
The ASA of an atom is the area of those
points on the surface of a sphere of radius
R which can contact the center of a
spherical solvent molecule that intersects
no other atoms.
R is the sum of the van der Walls radius
of the atom and the radius of the solvent
molecule (1.4˚A for water).
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ImplicitSolvationModels SASAmodels
Shrake-Rupley Algorithm
The Shrake-Rupley algorithm (1973) uses a discretization of the molecular
surface to estimate ASA:
92 points are distributed uniformly along a sphere centered at each
atom with radius R (defined on the previous slide).
The ASA is estimated by calculating the proportion of points that can
be contacted by a solvent molecule that intersects no other atoms.
Related methods approximate the surface using polyhedra.
Gradients of discretized ASA-estimates must be evaluated
numerically.
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ImplicitSolvationModels SASAmodels
Linear Combination of Pairwise Overlaps
Weiser et al. (1999) proposed an approximate analytical expression for
the ASA based on an inclusion-exclusion-like formula:
(cid:88) (cid:88)
A ≈ P S +P A + (P +P A )A
i 1 i 2 ij 3 4 ij jk
j∈N(i) j,k∈N(i)
k(cid:54)=j
S is the surface area of atom i.
i
A is the surface area of sphere i buried inside sphere j.
ij
N(i) is the neighbor list of atom i.
P - P were calculated using least squares regression.
1 4
The relative error is in the range 0.1−7.8%.
The resulting formula can be differentiated.
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ImplicitSolvationModels SASAmodels
Limitations of SASA Models
SASA models have several important limitations:
Solvation free energies are not linearly related to surface area, e.g.,
SASA overestimates hydration free energies of cyclic alkanes.
The solvation free energy calculated using SASA ignores the
electrostatic effects of the solvent.
SASA does not account for interactions between the solvent and
polar atoms that are buried in the interior of the macromolecule.
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