Transcript The Geometry of Biomolecular Solvation 1. Hydrophobicity Patrice Koehl Computer Science and Genome Center http://www.cs.ucdavis.edu/~koehl/ The Importance of Shape Sequence KKAVINGEQIRSISDLHQTLKK WELALPEYYGENLDALWDCLTG VEYPLVLEWRQFEQSKQLTENG AESVLQVFREAKAEGCDITI Structure Function ligand.

The Geometry of
Biomolecular Solvation
1. Hydrophobicity
Patrice Koehl
Computer Science and Genome
Center
http://www.cs.ucdavis.edu/~koehl/
The Importance of Shape
Sequence
KKAVINGEQIRSISDLHQTLKK
WELALPEYYGENLDALWDCLTG
VEYPLVLEWRQFEQSKQLTENG
AESVLQVFREAKAEGCDITI
Structure
Function
ligand
Enzyme – Substrate Binding
Substrate
(ligand)
+
Induced Fit
Enzyme
(receptor)
Co-factors may induce the fit: allostery
Ligand
Receptor
Co-factors bind
Co-factors
induce
conformational
Change: allostery
Ligand binds
Biomolecular Solvation
Stability of Protein Structures
Geometric Measures of Protein Structures
Applications
Accessibility
Binding sites
Biomolecular Solvation
Stability of Protein Structures
Geometric Measures of Protein Structures
Applications
Accessibility
Binding sites
Energy of a Protein
Bonded Interactions (chemistry)
Bonds, Angles, Dihedral angles
Non Bonded Interactions (“local” information)
van der Waals interactions, Electrostatics
Solvent (environment)
Most difficult
Solvent
Explicit or Implicit ?
Potential of mean force
A protein in solution occupies a conformation X with probability:
e
P( X , Y ) 
e


U  X ,Y 
kT
U  X ,Y 
kT
dXdY
The potential energy U can be decomposed as:
U ( X , Y )  U P ( X )  U S (Y )  U PS ( X , Y )
X: coordinates of the atoms
of the protein
Y: coordinates of the atoms
of the solvent
UP(X): protein-protein interactions
US(X): solvent-solvent interactions
UPS(X,Y): protein-solvent
interactions
Potential of mean force
We study the protein’s behavior, not the solvent:
PP ( X )   P( X , Y )dY
PP(X) is expressed as a function of X only through the definition:
PP ( X ) 
e
e


WT ( X )
kT
WT ( X )
kT
dX
WT(X) is called the potential of mean force.
Potential of mean force
The potential of mean force can be re-written as:
WT ( X )  U P ( X )  Wsol ( X )
Wsol(X) accounts implicitly and exactly for the effect of the solvent on the protein.
Implicit solvent models are designed to provide an accurate and fast
estimate of W(X).
Solvation Free Energy
Wsol
+
+
Sol
ch
W
W
Vac
ch
Wnp
Wsol  Welec  Wnp  W
sol
ch
W
vac
ch
  W
vdW
 Wcav 
The SA model
Surface area potential
N
Wcav  WvdW    k SAk
k 1
Eisenberg and McLachlan, (1986) Nature, 319, 199-203
Surface area potentials
Which surface?
Accessible
surface
Molecular
Surface
Hydrophobic potential:
Surface Area, or Volume?
Surface effect
(Adapted from Lum, Chandler, Weeks,
J. Phys. Chem. B, 1999, 103, 4570.)
Volume effect
“Radius of the molecule”
For proteins and other large bio-molecules, use surface
Biomolecular Solvation
Stability of Protein Structures
Geometric Measures of Protein Structures
Applications
Accessibility
Binding sites
Representations of Biomolecules
Cartoon
Space-filling Model
Computing the Surface Area
and Volume of a Union of Balls
Computing the Surface Area
and Volume of a Union of Balls
Power Diagram:
Computing the Surface Area
and Volume of a Union of Balls
Decomposition of the
Space-filling diagram
Computing the Surface Area
and Volume of a Union of Balls
i
i
Volume
Surface Area
N
A  4    i
i 1
i
2
i
4
V
3
N
 
i 1
3
i
i
Computing the Surface Area
and Volume of a Union of Balls
The weighted Delaunay triangulation is the dual of the power diagram
Computing the Surface Area
and Volume of a Union of Balls
The dual complex K is the dual of the decomposition of the space-filling diagram
Computing the Surface Area
and Volume of a Protein
K complex
Pocket
Protein
Delaunay Complex
http://www.cs.ucdavis.edu/koehl/ProShape/
Computing the Surface Area
and Volume of RNA
P4-P6 domain
Group I intron
K complex
Delaunay Complex
Pocket
Biomolecular Solvation
Stability of Protein Structures
Geometric Measures of Protein Structures
Applications
Accessibility
Binding sites
Experimental measures of accessibilities
Hydroxyl radical footprinting:
H5’’
H3’
H5’
H2’
H4’
H1’
HO2’
Residue number
Footprinting count / Ribose H accessibility
BINDING POCKETS IN 16S RIBOSOMAL RNA
Hygromycin B
PDB structure: 1HZN
BINDING POCKETS IN 16S RIBOSOMAL RNA
8Å
Probe Size
1.4 Å
BINDING POCKETS IN 16S RIBOSOMAL RNA