1. 9. Protein Docking

2. Prediction of protein-protein interactions
How do proteins interact?
Can we predict and manipulate those interactions?
Prediction of Structure – Docking
Prediction of Binding
Design – creation of new interactions

3. de novo Structure Prediction (ROSETTA) Docking (ROSETTADOCK)
Docking vs. ab initio modeling
de novo Structure Prediction (ROSETTA)
Docking (ROSETTADOCK)
ADEFFGKLSTKK…….
Sequence
Monomers +
Building Blocks:
backbone & side chains
Rigid body degrees of freedom
3 translation
3 rotation
CASP CAPRI
Structure
Complex

4. Monomers change structure upon binding to partner+ =
Solution 1: Tolerate clashes
Fast
Weak discrimination of correct solution + =
Solution 2: Model changes + =
Slow
Precise

5. Protein-protein docking
Sampling strategies
Fast detection of shape complementarity
Fast Fourier Transform (FFT): Cluspro
Geometric hashing: PatchDock
High-resolution docking: model changes explicitly
3. Rosettadock
Data-driven docking
Haddock
Template-based docking
COTH

6. Find shape complementarity: 1. Fast Fourier Transform (FFT)
Ephraim Katzir +

7. Find shape complementarity - FFT
Ephraim Katzir

8. Find shape complementarity: Fast Fourier Transform (FFT)
Ephraim Katzir
Test all possible positions of ligand and receptor:
For each rotation of ligand
(R)
evaluate all translations
(T) of ligand grid over
receptor grid
Y Translation
Correlation
X Translation
Discrete convolution
AXB = iFFT(FFT(A)*FFT(B)) z
= correlation product: can be calculated by FFT

9. Find shape complementarity: Fast Fourier Transform (FFT)
Ephraim Katzir
correlation product can be calculated by FFT:
Discrete convolution
AXB = iFFT( FFT(A) * FFT(B) )
Discrete convolution
AXB = iFFT(FFT(A)*FFT(B))

10. Find shape complementarity: Fast Fourier Transform (FFT)
Ephraim Katzir R R
Fast Fourier Transform
A=DFT(a)
Discretize
Correlation function
C=A*B
S=iDFT(C) L
Fast Fourier
Transform
B=DFT(b) L
Rotate L
Discretize
Surface
Interior 1
<0 for R
>0 for L
From

11. Find shape complementarity: Fast Fourier Transform (FFT)
Y Translation
Correlation
X Translation
Increases the speed by 107 L R
IFFT
Surface
Interior
Binding Site
From

12. Some FFT-based docking protocols
Zdock (Weng)
Cluspro & PIPER (Vajda, Camacho, Kozakov)
Molfit (Eisenstein)
DOT (TenEyck)
HEX (Ritchie) – FFT in rotation space

13. Piper – improved discrimination by cluster size
Low energy conformations will cluster
Clusters -> representatives
Clusters size
~ “region of attraction”
~ entropic contributions to free energy
Pk = Zk / Z, Z = Σj exp(-Ej /RT), Zk = Σj exp(-Ej /RT)
Z = N exp(-E /RT), Zk = K exp(-E /RT), Pk = Zk / Z= K / N
Kozakov Biophysical J., 2005, 89:867.

14. Piper – improved discrimination by cluster stability
Combine FFT (PIPER) with MC (Rosetta; see later in lecture ):
Re-sampling by Monte Carlo Minimization
7 Å
Stable cluster Unstable cluster
Kozakov. Proteins, 72 :993, 2008

15. Shape complementarity: 2
Shape complementarity: 2. Geometric hashing (patchdock, Wolfson & Nussinov)
Matching of puzzle pieces
Define geometric patches (concave, convex, flat)
Surface patch matching
Filtering and scoring
From

16. Hashing: alpha shapes Formalizes the idea of “shape”
In 2D an “edge” between two points is “alpha-exposed” if there exists a circle of radius alpha such that the two points lie on the surface of the circle and the circle contains no other points from the point set

17. Hashing – sparse surface representation
Slide from Jens Meiler

18. Docking with geometric hashing
PATCHDOCK (by Dina Schneidmann )
Fast and versatile approach
Speed allows easy extension to multiple protein docking, flexible hinge docking, etc
A extension of this protocol, FIREDOCK, includes side chain optimization (RosettaDock-like) – very flexible, fast and accurate protocol

19. 3. Explicit modeling of conformational changes in the monomers - High-resolution docking with Rosettadock
Random Start
Position
Random Start
Position
Low-Resolution Monte Carlo Search
Filters
High-Resolution Refinement
Predictions
Clustering
105

20. Choosing starting orientations
Euler angles are independent and guarantee non-biased search
Global search
Random Translation
Random Rotation (Euler Angles)
STARTING perturbation values:
-dock_pert n p r
Normal perturbation (A) def 3
Parallel perturbation (A) def 8
Rotation perturbation (degrees) def 8
(gaussian distribution with zero mean and pert std)
Low res perturb values:
10,50,0.7,5.0 (10 cycles of 50 steps; 0.7 translational magnitude, 5.0 rotational magnitude) initial magnitudes are adapted acc to success rate (high success: larger magnitudes: *1.1; low success rate (<0.5): smaller values: *0.9
High res perturb values:
50 cycles;
0.1 translation
0.05 rad rotation (around xyz axis) (~ 3degrees)
Minimization only if delta score –best <15
Full sc repack every 8th cycle (followed by rtmin)
Tilt direction [0..360o]
Tilt angle [0:90o]
Spin angle [0..360o]

21. Choosing starting orientations
Local Refinement
Translation 3Å normal, 8Å parallel
Rotation 80
Tilt direction [0±8o]
Tilt angle
Spin angle

22. Overview of docking algorithm
Random Start
Position
Low-Resolution Monte Carlo Search
Filters
High-Resolution Refinement
Predictions
Clustering
105

23. Low-resolution search
Perturbation
Monte Carlo search
Rigid body translations and rotations
Residue-scale interaction potentials
Protein representation:
backbone atoms + average centroids
Low res perturb values:
10,50,0.7,5.0 (10 cycles of 50 steps; 0.7 translational magnitude, 5.0 rotational magnitude) initial magnitudes are adapted acc to success rate (high success: larger magnitudes: *1.1; low success rate (<0.5): smaller values: *0.9
Mimics physical diffusion process

24. Overview of docking algorithm
Random Start
Position
Low-Resolution Monte Carlo Search
Filters
High-Resolution Refinement
Predictions
Clustering
105

25. High resolution optimization: Monte Carlo with Minimization (MCM)
Cycles of iterative optimization
START
Random
perturbation
Side chain optimization
Energy
Rigid body orientations
Random perturbation
Side chain
optimization
Rigid body minimization
In the high-resolution refinement step the side chain atoms are added back.
Side chains are selected from a rotamer library that contains a discrete set of likely conformations.
A full atom energy function calibrated on different Rosetta protocols is now used to evaluate and optimize models. It contains mainly van der waals attractive and repulsive terms, and in addition accounts for solvation and hydrogen bonding.
We then use monte-carlo with minimization, in short MCM, to search the minimum energy conformation in the vast space of possible configurations.
HANDS Let’s try to find the nearby optimum of a given RB orientation. For this we make a small change in the RB orientation. This might lead to clashes. Rearrangement of the side chains at the interface can sometimes relieve those clashes. Only then we further optimize the RB orientation. This mimics conformational changes upon binding at the side chain level. At the end of such a step, we evaluate whether a better conformation has been obtained.
Let’s look at how the monte-carlo cycle that I just described looks on the energy landscape:
Each of the possible rigid body orientations of the two monomers can be characterized by its energy, and its distance to some arbitrary reference.
Each monte carlo cycle starts with a small change of the protein’s relative orientation in our search for the minimum.
Instead of minimizing the RB orientation directly however, we first allow the monomer conformation to adapt to the new orientation, by optimizing the side chain conformations. This allows to relieve a clash that involves the side chains at the interface. This of course also changes the energy landscape: The energy of a given RB orientation is changed if the monomer conformations are different.
We now optimize the rb orientation by deepest descent minimization. This locates a minimum that might not have been apparent in the previous landscape.
Finally, we apply the MC criterion, accepting in addition to downward moves also moves that increase the energy, by a boltzman-dependent probability.
Repeated cycles of this procedure allow us to efficiently find the minimum energy conformation near the starting point. MC
Rigid body
minimization
FINISH

26. Overview of docking algorithm
Random Start
Position
Filters
Low-Resolution Monte Carlo Search
High-Resolution Refinement
Clustering
Predictions
105

27. Clustering Compare all top-scoring decoys pairwise
Cluster decoys hierarchically
Decoys within e.g. 2.5Å form a cluster
Represents
ENTROPY

28. Assessment 1: Benchmark studies
Benchmark set contains 54 targets for which
bound and unbound structures are known
Bound-Bound
Start with bound complex structure, but remove the side chain configurations so they must be predicted
α-chymotrypsin
+ inhibitor
subtilisin + inhibitor
trypsin + inhibitor
barnase + barstar
Unbound-Unbound
Start with the individually-crystallized component proteins in their unbound conformation
Bound-Unbound (Semibound)
lysozyme + antibodies
hemagglutinin
+ antibody
actin + deoxyribonuclease I
subtilisin + prosegment

29. Assessment of method on benchmark (54 proteins, Gray et al., 2003)
Overall performance
funnel - 3/5 top-scoring models within 5A rmsd
Bound Docking
Perturbation1
42/54
Unbound Docking Perturbation2
32/54
Unbound Docking
Global3
28/32
……..
More than three of top five decoys (by score) that have rmsd less than 5 Å
More than three of top five decoys (by score) that predict more than 25% native residue contacts
The rank of the first cluster with >25% native residue contacts

30. Limitation of “rotamer-based” modeling
Near-native model with clash
Non-native model without clash
Trp 172
Trp 215
Orange and red: native complex; Blue: docking model.
PDB code: 1CHO

31. RosettaDock simulation
1 model/simulation: energy vs RMSD (structural similarity to starting model)
Final model selected based on energy (and/or sample density)
At the end of a simulation, we have optimized a large number of random orientations, each yielding a model that is characterized by its energy (y-axis) and its distance to the starting model (x-axis). The latter is measured as the RMSD between the ligands (the second partner) when the receptor structure is superimposed, or by looking at the same measure calculated for the interface residues only.
This is a typical plot. The background contains a large number of different orientations, all with similar energy, while a small number of similar models that contain significantly better energy values are clustered together at a similar RMSD value.
This is the signature of a likely correct prediction, as will become clear in the following.
The low-energy conformations that are significantly lower in energy are then further characterized by local optimization.
Energy
Rigid body orientations:
RMSD to arbitrary starting structure (Å)

32. RosettaDock simulation
Initial Search
Refinement
Energy
(Å)
RMSD to arbitrary starting structure
RMSD to starting structure of refinement

33. CAPRI Target 12 Cohesin-Dockerin
Side chain flexibility is important
CAPRI Target 12 Cohesin-Dockerin
Dockerin
0.27Å interface rmsd
87% native contacts
6% wrong contacts
Overall rank 1
Cohesin
red,orange– xray
blue – model;
green – unbound
Carvalho et. al (2003) PNAS

34. Details of T12 interface Dockerin Cohesin red,orange– xray
blue - model

35. Similar landscapes for different Rosetta predictions
Docking energy landscape
Folding energy landscape
Energy function describes well principles underlying the correct structure of monomers and complexes
Its not trivial that two (or three) pretty different questions can be addressed by the same energy function, and this indicates that it adequately describes some basic physical principles that govern the protein structure and protein-protein interactions.

36. A Challenging Target RF1-HEMK (T20)
Challenge:
Large complex
RF1 to be modeled from RF2
Disordered Q-loop
Hope:
Q235 methylated
A Gln analog in HemK crystal
Strategy:
Trimming – Docking – Loop Modeling - Refining
Q252
RF1
loop1
loop2
Q-loop
Q-235
HemK
Q252
RF1
loop1
loop2
Q-loop
Q-235
HemK
Q252
Q-235
HemK
RF1
loop1
loop2
Q-loop
Q252
Q-235
HemK
RF1
Keys to success: Location of interface with truncated protein
Separate modeling of large conformational change in key loop

37. Prediction of large conformational change
Gln235
GLN235 C atom shift:14.13Ǻ to 3.91 Ǻ
Q-loop global C rmsd: 11.8 Ǻ to 4.8 Ǻ
I_rmsd 2.34 Ǻ
F_nat 34.2%
Red, orange – bound; Green,– unbound; Blue -- model

38. Docking with backbone minimization
2SNI N 1 C 1’
Fold
tree
Interface energy
START
random
perturbation
repack
minimization
FINISH
Red: bound rigid
Green: unbound rigid
Blue: unbound flexible
Interface RMSD
# of “hits” in top 10 models
Rigid-body
Backbone
Sidechain
Docking Monte Carlo Minimization (MCM)

39. Docking with loop minimization1 1’ C 2 2’ x
Fold-tree
Minimize rigid-body and loop simultaneously
Correctly predicted loop conformation
Flexible Docking
All-atom energy
Interface RMSD
Red, orange – bound (1T6G, Sansen, S. et al, J.B.C.(2004));
Blue – model; Green – unbound (1UKR, Krengel U. et al, JMB (1996))

40. Docking with loop rebuilding
Ligand RMSD
All-atom energy
Bound rigid
1BTH
unbound rigid
unbound flexible loop

41. Flexible backbone protein–protein docking using ensembles
Incorporate backbone flexibility by using a set of different templates
Generation of set of ensembles: with Rosetta relax protocol, from NMR ensembles, etc
Fig. 1. Ligand ensemble generation and CS. (a) Crystal structures are idealized and then relaxed at low and high resolutions to generate an ensemble of 10 structures. (b) Conformers in an NMR ensemble are idealized and refined at high resolution only. (c) During low-resolution docking, conformers are superposed along the current conformer's interface residues, and a conformer is selected from a partition function using Boltzmann-weighted energies.
Chaudhury & Gray, (2008)

42. Sampling among conformers during docking
Exchange between templates during protocol
Fig. 2. The flexible docking algorithm. The low-resolution phase models the formation of an encounter complex, and the high-resolution phase models its transition to a bound complex. CS and CS/IF docking include the CS step (green box). IF and CS/IF docking include backbone minimization (orange box).

43. Evaluation of 4 different protocols
key-lock (KL) model
rigid-backbone docking
2. conformer selection (CS) model
ensemble docking algorithm
induced fit (IF) model
energy-gradient-based backbone minimization
4. combined conformer selection/induced fit (CS/IF) model
Can teach us about the possible binding mechanism (e.g. induced fit vs key-lock)
Histogram of hit quality (quality of the top-ranked decoy for all runs, with at least 5 of the 10 top-scoring decoys being of medium or high quality) for each docking method for (a) crystal structure targets and (b) NMR targets. CAPRI criteria: high-quality decoys are shown in brown, and medium-quality decoys are shown in orange.
Brown: high-quality decoys
Orange: medium-quality decoys

44. RosettaDock4.0 Improvement due to better sampling and scoring:
Adaptive conformer selection (ACS):
Ensemble docking: conformer swapping rate adapted
(few/many acceptances  more/less sampling)
Replace low-resolution centroid score with Motif-Dock Score (MDS, using residue-pair transform score, RPX):
Parameters: aa1,aa2, 6D transformation for superimposing N– Cα–C backbone atoms onto each other (for Cα < 10A)
Lookup in pre-tabulated database
Fig. 2. The flexible docking algorithm. The low-resolution phase models the formation of an encounter complex, and the high-resolution phase models its transition to a bound complex. CS and CS/IF docking include the CS step (green box). IF and CS/IF docking include backbone minimization (orange box).
Marze et al. Bioinformatics 2018

45. RosettaDock4.0 Calibration: Use ensembles for ligand and receptor:
Rosetta Rosetta 4.0
Calibration: Use ensembles for ligand and receptor:
40 Backrub
30 relax
30 Normal mode
 8x more near-native models retained after low-resolution step
Fig. 2. The flexible docking algorithm. The low-resolution phase models the formation of an encounter complex, and the high-resolution phase models its transition to a bound complex. CS and CS/IF docking include the CS step (green box). IF and CS/IF docking include backbone minimization (orange box).
Marze et al. Bioinformatics 2018

46. RosettaDock4.0
Improved docking at low-resolution step ( faster), resulting in overall improvement (mainly difficult cases)
N5: # of near-native models (interface RMSD <5A) among top5 scoring
Fig. 2. The flexible docking algorithm. The low-resolution phase models the formation of an encounter complex, and the high-resolution phase models its transition to a bound complex. CS and CS/IF docking include the CS step (green box). IF and CS/IF docking include backbone minimization (orange box).
Marze et al. Bioinformatics 2018

47. RosettaDock - summary
First program to introduce general (side chain) flexibility during docking
Advanced the docking field towards unbiased high-resolution modeling
Many other protocols have since then incorporated RosettaDock as a high-resolution final step
Targeted introduction of backbone flexibility can improve modeling dramatically

48. 4. Data-driven docking Challenges:
Large conformational space to sample
Conformational changes of proteins upon binding
Approach: restrict search space by previous information
HADDOCK (High Ambiguity Driven protein-protein Docking)

49. Scheme of Haddock Bonvin, JACS 2003
Information about complex can be retrieved from several sources

50. Haddock computational scheme
Derive Ambiguous Interaction Restraints (AIRs):
Active residues: involved in interaction, and solvent accessible
Passive residues: neighbors of active residues
Create CNS restraints file (Used in NMR structure determination)
Rational:
include AIRs in energy function
find protein complex structure with minimum energy
Similar to
solving a structure by NMR
Homology modeling with constraints (e.g. Modeler)

51. Overview of Haddock Start Position Rigid body energy minimization:
rotational minimization
rotational & translational
Align molecules if anisotropic data is available
Satisfy maximum number of AIC
Retain top200
Predictions
Semi-flexible simulated annealing (SA)
High temperature rigid body search
Rigid body SA
Semi-flexible SA with flexible side-chains at the interface
Semi-flexible SA with fully flexible interface (both backbone and side-chains)
Explain 105
Flexible explicit solvent refinement
Improves energy ranking
Clustering

52. 5. Template-based docking: COTH
Szilágyi & Zhang (2014). Current Opinion in Structural Biology, 24:10
Mukherjee & Zhang (2011). Structure 19:955

53. Docking – Summary & Outlook
Efficient search using
fast sampling techniques (e.g. FFT, Geometric hashing), or/and
Restraints to relevant region (e.g. biological constraints, etc)
Or: skip this and perform template-based docking 
Challenge: conformational changes in the partners
Introduction of flexibility improves model quality
Full side chain flexibility (Rosetta)
Targeted introduction of backbone flexibility
Larger changes can be incorporated using techniques such as Normal Mode Analysis