Dec. 2014
Molecular Docking – Part II
Docking Problem
• Input: A pair of molecules in their
native conformation
Flexible Docking
• Goal: Find their correct association as
it appears in nature
T
??
Dec 2014
H. J. Wolfson -INRIA
H. J. Wolfson -INRIA
Small Molecule Flexibility
Dec 2014
Docking and Flexibility
 Which types of molecules are docked?
 Protein + small molecule
 Protein + protein
…
 Wh
Whichh types off flexibility
fl b l are taken
k into account?
 Large-scale hinge-bent motions
 Small-scale side-chain motions
 Small molecule torsional flexibility
…
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
 Which molecules are considered as flexible?
 Receptor, ligand or both
H. J. Wolfson -INRIA
Dec 2014
1
Dec. 2014
Handling Protein Backbone
Flexibility in Docking
Shear motion
Hinge motion
Fast Interaction REfinement
in molecular DOCKing
Flexible loop motion
N. Andrusier, R. Nussinov, H. J. Wolfson, FireDock: Fast Interaction
Refinement in Molecular Docking, Proteins, 69, 139—159, (2007).
H. J. Wolfson -INRIA
Dec 2014
General Docking Flow
H. J. Wolfson -INRIA
Dec 2014
Flexible Refinement Motivation
 Proteins are in constant motion
 Both backbone and side-chains change conformation
 The induced-fit model:
Rigid-Body Docking
 Correct docking of the
Rigid-body
candidates
‘unbound’ proteins may
cause steric clashes
Refinement
 Refine and re-score
rigid-docking solutions
Complex Hypotheses
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
2
Dec. 2014
Refinement Flow
Goals
1. Top ranking of near native solutions
2. High-accuracy
g
y solution
Rigid-Body Docking
Side-Chain Optimization
Rigid-body
candidates
Refinement
Rigid-Body Optimization
Complex Hypotheses
Ranking
1
3. Fast
2
.
.
. Dec 2014
H. J. Wolfson -INRIA
H. J. Wolfson -INRIA
Dec 2014
The Refinement Stages
The FireDock Flow
Side-Chain Optimization
PatchDock
Preprocessing
thousands of
candidates
25 top-ranked
candidates
RISCO – clashing
residues only
Restricted
Interface Side-Chain Optimization
Atomic Radii Scaling = 0.8
Ri id B d Optimization
Rigid-Body
O ti i ti
FISCO – all residue
optimization
Ranking
Full
Interface Side-Chain Optimization
Atomic Radii Scaling = 0.85
Rigid-Body Optimization
Rigid-Body Optimization
Ranking
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Ranking
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
3
Dec. 2014
Interface Side-Chain Optimization
Pair-wise
energy
Graph Representation:
Choosing one node per residue
to minimize the weight of the induced
sub-graph
sub
graph
The Linear Programming (LP)
Technique
 A technique for optimization of a linear function
 Subject to linear equality and inequality constraints.
 Can be solved by a fast (polynomial time) method, supported
Self
energy
by an efficiently implemented software package (CPLEX).
The Side Chain
Optimization Problem
was proven to be
Dec 2014
NP-hard
GMEC = Global Minimal Energy Conformation
H. J. Wolfson -INRIA
Formulation of ISCO as LP
H. J. Wolfson -INRIA
Rigid-Body Optimization
rotamer r was selected for residue i
1
y ir  
0 rotamer r was not selected for residue i
Ranking
V – set of movable residues
N(i) – interacting residues of residue i
H.J. Wolfson - INRIA



Side-Chain Optimization
Rigid-Body Optimization
H. J. Wolfson -INRIA
Why?

the edge (ir , js ) is in the induced graph
1
xir js  
0 the edge (ir , js ) is not in the induced graph
0 ≤ xir ≤ 1
0 ≤ yir ≤ 1
Dec 2014
Soft rigid-body docking
Unresolved clashes
Surface was changed
g after ISCO
How?



Energy Minimization
6 Degrees of freedom
Not linear!
In 99.9% the LP
solution is integral
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
4
Dec. 2014
Monte Carlo Minimization
The Refinement Stages
Random Perturbation of Ligand
Side-Chain Optimization
Local Energy Minimization
Ri id B d Optimization
Rigid-Body
O ti i ti
P(E,E’)
accepted
Ranking
rejected
Metropolis Criterion:
Return to the previous position
P( E , E ' )  min{ exp(
E  E'
),1}
CbT
x50
H. J. Wolfson -INRIA
Dec 2014
The Binding Model
H. J. Wolfson -INRIA
Dec 2014
Atomic Contact Energy
• ACE - desolvation free energies required to transfer atoms
from water to a protein’s interior.
• Estimated from known crystal structures.
• Introduced by Miyazawa & Jernigan 96’. Zhang et al. 97’
extended this approach to the atomic contacts.
• Calculated over atoms pairs within 6Å
Å distance:
 Binding score:
 ACE
 Electrostatics
 Hydrophobic interactions
GACE   eij
 van der Waals
…
i
j
eij - effective free energy change when a bond between
two atoms of type i and j is replaced by solute-solvent
bonds.
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
H. J. Wolfson -INRIA
eij  
nij n00
ni 0 n j 0
Dec 2014
5
Dec. 2014
π-stacking & Aliphatic Interactions
Electrostatics
 Electrostatics
 Epipi - π-π interactions
 Coulomb:
Eelec   332
(Phenylalanine, Tyrosine, Tryptophan, Histidine, Proline)
 Ecatpi - cation-π interactions
qi q j
dij2
i, j
(Arginine, Lysine) – (Phenylalanine, Tyrosine, Tryptophan)
Gl t i & A
Glutamic
Aspartic
ti A
Acids
id
 separated to attractive/repulsive and
A i i &L
Arginine
Lysine
i
 Ealiph - aliphatic interactions
(Leucin, Isoleucin, Valine)
short/long range categories
 Hydrogen Bonds
 r
EHB    5  0

ij   d ij

12

r
  6  0

 dij
10







where 2.74 Å < dij < 3.5 Å, r0 = 2.9 Å
H. J. Wolfson -INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
Misura et al., 2004
van der Waals
“Insideness” Term
 Lennard-Jones 6-12 potential with linear repulsion as in Gray
et al., 2003
For enzyme/inhibitor concave interfaces
number of contacts
to avoid bigg penalty
p
y for small clashes
 based on CHARMM19
insideness
CM of blues
WCM
of blues
insideness
CM of pinks
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
6
Dec. 2014
Binding Free Energy
G  G C  (G R  G L )
C
L
R
G  Ginterf_inter
 Ginterf_intra
 Ginterf_intra
H. J. Wolfson -INRIA
Dec 2014
Ranking – energy function
H. J. Wolfson -INRIA
Dec 2014
Results
Antibody
Antigen
complex
☺ Significant improvement over PatchDock ranking
☺ Successful for EI and semi-unbound AA cases
Enzyme
Inhibitor
complex
Unsuccessful for unbound AA cases
☺ On the benchmark 1.0 cases:
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
RosettaDock
PatchDock+FireDock
25/43 (3.61 Å)
30/43 (3.35 Å)
☺
Successful
ranking in CAPRI “scorers” category. Dec 2014
H. J. Wolfson
-INRIA
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Dec. 2014
Contribution of Scoring Terms
Time Efficiency
FISCO LP
H. J. Wolfson -INRIA
Dec 2014




FISCO ILP
In RISCO LP/ILP is very fast (small number of variables)
In 99.9 % of the cases the LP solution is integral
RBO is a bottle-neck
Pentium 4 CPU 3.2GHz 1GB RAM
H. J. Wolfson -INRIA
Dec 2014
Conclusions
 Improves both accuracy and ranking of rigid docking
FiberDock
solutions (created by PatchDock)
 Typical running time is 4 seconds per candidate
Flexible Induced-fit Backbone
Refinement in Molecular
Docking
 Assumes rigidity of proteins backbone.
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
E. Mashiach, R. Nussinov and H. J. Wolfson. FiberDock: Flexible induced-fit backbone
refinement in molecular docking. Proteins 2009;78(6):1503-1519.
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Dec. 2014
Anisotropic Network Model (ANM)
Normal Modes Analysis (NMA)
 Simplified spring models of proteins
 Given a single conformation,
NMA calculates a set of vectors (3N) which describes the
flexibility of a protein.
(3,8,1)
 NMs span the conformational space
(4,6,2)
(9,1,1)
(7,8,4)
 The coefficients represent the amplitudes
More details…
Tama and Sanejouand (2001)
Back…
Hinsen (1998)
Figure from Andrusier et al. (2008)
NMA - Advantages
NMA - Disadvantages
 Similarity to true protein motions
 Describes only one conformation with minimum energy
 Conformations can change continuously
 The lowest frequency modes contribute the most to a
conformational change
(domains rearrangement)
Hinsen (1998)
H.J. Wolfson - INRIA
May, M. Zacharias (2005)
Hinsen (1998)
Petrone and Pande (2006)
Petrone and Pande (2006)
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Dec. 2014
The Main Idea
NMA - Disadvantages
 Flexible docking refinement which models both backbone
 Describes only one conformation with minimum energy
and side-chain flexibility.
 Can create distorted conformations
 High complexity in memory (O(N2)) and in CPU time (O(N3))
 Existing docking methods model backbone flexibility by
using only the first few modes. We use an a-priori
unlimited number of normal modes.
 Iteratively apply the most relevant modes on the flexible
protein.
 The relevancy of a mode is calculated according to its
correlation with the chemical forces applied on each
atom.
Hinsen (1998)
Petrone and Pande (2006)
The Docking
Refinement
Algorithm:
The Backbone Refinement Method:
Adopted from
FireDock
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
10
Dec. 2014
The Backbone Refinement Method:
Correlation Measurement
 The correlation between the forces (F) which are applied on
the Cα atoms and a certain normal mode (Vi) is calculated in
the following way:
Dot
D t product:
d t
 Good correlation indicates that the directions of the forces
suit the directions of the normal mode vectors.
H. J. Wolfson -INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
Structure Minimization
Changing the Protein Conformation
 We use the BFGS quasi-Newton algorithm
 NMs often distort the protein structure
to locate a local energy minimum
in the direction of the chosen
((most relevant)) normal modes.
 Finds the amplitude which
produces a local energy minimum.
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
11
Dec. 2014
Changing the Protein Conformation
The Backbone Refinement Method:
 NMs often distort the protein structure
 Goals:
 Don’t change bonds length and angles
 Change only φ and ψ torsion angles
 Answer:
Use a modification of the CCD robotics algorithm
by Canutescu and Dunbrack, 2003.
H. J. Wolfson -INRIA
Dec 2014
Monte Carlo Minimization
H. J. Wolfson -INRIA
Dec 2014
The Backbone Refinement Method:
Random Perturbation of Ligand
Local Energy Minimization
P(E,E’)
accepted
rejected
Metropolis Criterion:
Return to the previous position
P( E , E ')  min{exp(
E E'
),1}
k bT
x10
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
12
Dec. 2014
Scoring Function
Contains the binding Van der Waals energy value
(EVdW) and a penalty term which depends on the
amount of protein deformation.
The Docking
Refinement
Algorithm:
The penalty term prevents the algorithm from
returning distorted solutions.
H. J. Wolfson -INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
Test III
Results
 For each test case we refined the first 500 rigid
docking solutions of PatchDock.
Test III: Docking refinement starting from rigid-body docking
candidates
 The
Th results
lt off th
the refinement
fi
t with
ith Fib
FiberDock
D k andd
FireDock were compared
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
H. J. Wolfson -INRIA
Dec 2014
13
Dec. 2014
Test III - Results
H. J. Wolfson -INRIA
Dec 2014
Bound receptor
PatchDock model
FiberDock model
H. J. Wolfson -INRIA
Ligand in native position
Dec 2014
H. J. Wolfson -INRIA
1E6E
Dec 2014
Test III - Results
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
14
Dec. 2014
FiberDock web-server
H. J. Wolfson -INRIA
H.J. Wolfson - INRIA
Dec 2014
http://bioinfo3d.cs.tau.ac.il/FiberDock/
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