Title: Hydropathyphobicityphilicity
1Hydropathy/phobicity/philicity
 One of the most commonly used properties is the
suitability of an amino acid for an aqueous
environment  Hydropathy Hydrophobicity
 degree to which something is water hating or
water fearing  Hydrophilicity
 degree to which something is water loving
2Hydrophobicity/Hydrophilicity Tables
 Describe the likelihood that each amino acid will
be found in an aqueous environment  one value
for each amino acid  Commonly used tables
 KyteDoolittle hydropathy
 HoppWoods hydrophilicity
 Eisenberg et al. normalized consensus
hydrophobicity
3KyteDoolittle hydropathy
4Example Hydrophilicity Plot
This plot is for a tubulin, a soluble cytoplasmic
protein. Regions with high hydrophilicity are
likely to be exposed to the solvent (cytoplasm),
while those with low hydrophilicity are likely to
be internal or interacting with other proteins.
5Amphiphilicity/Amphipathicity
 A structural domain of a protein (e.g., an
?helix) can be present at an interface between
polar and nonpolar environments  Example Domain of a membraneassociated protein
that anchors it to membrane  Such a domain will ideally be hydrophilic on one
side and hydrophobic on the other  This is termed an amphiphilic or amphipathic
sequence or domain
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7Screenshot of a phospholipid bilayer in the
process of its modeling. Shown is a computational
cell consisting of 96 PhCh molecules and 2304
water molecules which on the whole make up 20544
atoms.
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9Average number of hydrogen bonds within the first
water shell around an ion
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11Molecular Dynamics Introduction
 Newtons second law of motion
12Molecular Dynamics Introduction
 We need to know
 The motion of the
 atoms in a molecule, x(t)
 and therefore,
 the potential energy, V(x)
13Molecular Dynamics Introduction
 How do we describe the potential energy V(x) for
a  molecule?
 Potential Energy includes terms for
 Bond stretching
 Angle Bending
 Torsional rotation
 Improper dihedrals
14Molecular Dynamics Introduction
 Potential energy includes terms for (contd.)
 Electrostatic
 Interactions
 van der Waals
 Interactions
15Molecular Dynamics Introduction
 In general, given the values x1, v1 and the
potential energy V(x), the molecular trajectory
x(t) can be calculated, using,
16How a molecule changes during MD
17Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
18Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
19Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
20Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
21Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
22Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
23Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
Repulsion
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
Mixed terms
24Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
Repulsion
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
Mixed terms
25Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
Repulsion
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
Attraction

Mixed terms
26Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
Repulsion
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
Attraction
Mixed terms
27Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
Repulsion
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
Attraction

Mixed terms
28Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
Repulsion
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
Attraction
u(2)
u(2)

u(N)
Mixed terms
29Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
Repulsion
 UvdW van der Waals
 Uel electrostatic
 Upol polarization
 Ustr stretch
 Ubend bend
 Utors torsion
 Ucross cross
Attraction
u(2)
u(2)

u(N)

Mixed terms
30Modeling Potential energy
31Modeling Potential energy
32Stretch Energy
 Expand energy about equilibrium position
 Model fails in strained geometries
 better model is the Morse potential
(neglect)
minimum
define
harmonic
Morse
dissociation energy
force constant
33Bending Energy
q
 Expand energy about equilibrium position
 improvements based on including higherorder
terms  Outofplane bending
(neglect)
minimum
define
harmonic
u(4)
c
34Torsional Energy
f
 Two new features
 periodic
 weak (Taylor expansion in f not appropriate)
 Fourier series
 terms are included to capture appropriate
minima/maxima  depends on substituent atoms
 e.g., ethane has three mimumenergy conformations
 n 3, 6, 9, etc.
 depends on type of bond
 e.g. ethane vs. ethylene
 usually at most n 1, 2, and/or 3 terms are
included
35Van der Waals Attraction
 Correlation of electron fluctuations
 Stronger for larger, more polarizable molecules
 CCl4 gt CH4 Kr gt Ar gt He
 Theoretical formula for longrange behavior
 Only attraction present between nonpolar
molecules  reason that Ar, He, CH4, etc. form liquid phases
 a.k.a. London or dispersion forces

36Van der Waals Repulsion
 Overlap of electron clouds
 Theory provides little guidance on form of model
 Two popular treatments
 inverse power exponential
 typically n 9  12 two parameters
 Combine with attraction term
 LennardJones model Exp6
a.k.a. Buckingham or Hill
Beware of anomalous Exp6 shortrange attraction
Exp6 repulsion is slightly softer
37Electrostatics 1.
 Interaction between charge inhomogeneities
 Modeling approaches
 point charges
 point multipoles
 Point charges
 assign Coulombic charges to several points in the
molecule  total charge sums to charge on molecule (usually
zero)  Coulomb potential
 very long ranged
38Electrostatics 2.
 At larger separations, details of charge
distribution are less important  Multipole statistics capture basic features
 Dipole
 Quadrupole
 Octopole, etc.
 Point multipole models based on longrange
behavior  dipoledipole
 dipolequadrupole
 quadrupolequadrupole
Vector
Tensor
Axially symmetric quadrupole
39Polarization
 Charge redistribution due to influence of
surrounding molecules  dipole moment in bulk different from that in
vacuum  Modeled with polarizable charges or multipoles
 Involves an iterative calculation
 evaluate electric field acting on each charge due
to other charges  adjust charges according to polarizability and
electric field  recompute electric field and repeat to
convergence  Reiteration over all molecules required if even
one is moved

40Polarization
Approximation
Electrostatic field does not include
contributions from atom i
41Common Approximations in Molecular Models
 Rigid intramolecular degrees of freedom
 fast intramolecular motions slow down MD
calculations  Ignore hydrogen atoms
 united atom representation
 Ignore polarization
 expensive nbody effect
 Ignore electrostatics
 Treat whole molecule as one big atom
 maybe anisotropic
 Model vdW forces via discontinuous potentials
 Ignore all attraction
 Model space as a lattice
 especially useful for polymer molecules
Qualitative models
42Molecular Dynamics Introduction
 Equation for covalent terms in P.E.
43Molecular Dynamics Introduction
 Equation for nonbonded terms in P.E.
44DNA in a box of water
45SNAPSHOTS
46Protein dynamics study
 Ion channel / water channel
 Mechanical properties
 Protein stretching
 DNA bending
Movie downloaded from theoreticla biophysics
group, UIUC
47Solvent dielectric models
Effetive dielectric constant