Hydropathyphobicityphilicity

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Hydro-pathy/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

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Hydrophobicity/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
• Kyte-Doolittle hydropathy
• Hopp-Woods hydrophilicity
• Eisenberg et al. normalized consensus
  hydrophobicity

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Kyte-Doolittle hydropathy
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Example 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.
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Amphiphilicity/Amphipathicity

• A structural domain of a protein (e.g., an
  ?-helix) can be present at an interface between
  polar and non-polar environments
• Example Domain of a membrane-associated 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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Screenshot 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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Average number of hydrogen bonds within the first
water shell around an ion
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Molecular Dynamics Introduction

• Newtons second law of motion

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Molecular Dynamics Introduction

• We need to know
• The motion of the
• atoms in a molecule, x(t)
• and therefore,
• the potential energy, V(x)

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Molecular 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

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Molecular Dynamics Introduction

• Potential energy includes terms for (contd.)
• Electrostatic
• Interactions
• van der Waals
• Interactions

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Molecular Dynamics Introduction

• In general, given the values x1, v1 and the
  potential energy V(x), the molecular trajectory
  x(t) can be calculated, using,

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How a molecule changes during MD
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Contributions 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

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Contributions 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

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Contributions 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

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Contributions 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

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Contributions 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

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Contributions 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

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Contributions 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
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Contributions 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
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Contributions 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
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Contributions 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
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Contributions 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
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Contributions 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
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Contributions 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
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Modeling Potential energy
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Modeling Potential energy
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Stretch 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
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Bending Energy
q

• Expand energy about equilibrium position
• improvements based on including higher-order
  terms
• Out-of-plane bending

(neglect)
minimum
define
harmonic
u(4)
c
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Torsional 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 mimum-energy 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

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Van der Waals Attraction

• Correlation of electron fluctuations
• Stronger for larger, more polarizable molecules
• CCl4 gt CH4 Kr gt Ar gt He
• Theoretical formula for long-range behavior
• Only attraction present between nonpolar
  molecules
• reason that Ar, He, CH4, etc. form liquid phases
• a.k.a. London or dispersion forces

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Van 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
• Lennard-Jones model Exp-6

a.k.a. Buckingham or Hill
Beware of anomalous Exp-6 short-range attraction
Exp-6 repulsion is slightly softer
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Electrostatics 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

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Electrostatics 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 long-range
  behavior
• dipole-dipole
• dipole-quadrupole
• quadrupole-quadrupole

Vector
Tensor
Axially symmetric quadrupole
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Polarization

• 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
• re-compute electric field and repeat to
  convergence
• Re-iteration over all molecules required if even
  one is moved

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Polarization
Approximation
Electrostatic field does not include
contributions from atom i
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Common 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 n-body 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
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Molecular Dynamics Introduction

• Equation for covalent terms in P.E.

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Molecular Dynamics Introduction

• Equation for non-bonded terms in P.E.

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DNA in a box of water
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SNAPSHOTS
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Protein dynamics study

• Ion channel / water channel
• Mechanical properties
• Protein stretching
• DNA bending

Movie downloaded from theoreticla biophysics
group, UIUC
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Solvent dielectric models
Effetive dielectric constant