1. AUTODOCK An Automated Docking Software for Predicting Optimal Protein-Ligand InteractionBy
Susan McClatchy, Milind Misra,
Chandreyee Mukherjee, Indu Shrivastava

2. Introduction
Chandreyee Mukherjee

3. Automated Docking: Importance
Interaction between biomolecules lie at the core of all metabolic processes and life activities
The number of solved protein structures available in the databases is expanding exponentially
To understand their functions it is essential to elucidate the interaction mechanisms between the different molecules
Primary importance lies in rational drug design
Depending upon the success of the docked molecules the docking ligand may be redesigned or its structure further refined.
Also important in the area of immunology to study antigen-antibody interaction.

4. Inhibitor bound to active site of HIVPR
Surface structure of HIVPR with bound
inhibitor

5. What is docking?
Prediction of the optimal physical configuration and energy between two molecules
The docking problem optimizes:
Binding between two molecules such that their orientation maximizes the interaction
Evaluates the total energy of interaction such that for the best binding configuration the binding energy is the minimum
The resultant structural changes brought about by the interaction

6. Categories of docking Protein-Protein Docking:
Both molecules are rigid
Interaction produces no change in conformation
Similar to lock-and key model
Protein-Ligand Docking:
Ligand is flexible but the receptor protein is rigid
Interaction produces conformational changes in ligand

7. Protein-Protein Docking
Protein-Ligand Docking
optimized

8. Docking uses a “search and score” method
It involves:
Finding useful ways of representing the molecules and molecular properties.
Exploration of the configuration spaces available for interaction between ligand and receptor.
Evaluate and rank configurations using a scoring system, in this case the binding energy
However, since it is difficult to evaluate the binding energy because the binding sites may not be easily accessible, the binding energy is modeled as follows:
∆G bind= ∆Gvdw + ∆Ghbond + ∆Gelect + ∆G conform+ ∆G tor + ∆G sol

9. The AutoDock Software Search Algorithms used:
Developed by AJ Olson’s group in 1990.
AutoDock uses free energy of the docking molecules using 3D potential-grids
Uses heuristic search to minimize the energy.
Search Algorithms used:
Simulated Annealing
Genetic Algorithm
Lamarckian GA (GA+LS hybrid)

10. Algorithms Overview Simulated Annealing Genetic Algorithm
Based on temperature effects
Start with high temperature and global search
Lower temperature local search
Genetic Algorithm
Charles Darwin’s Theory of Evolution
Genotype Phenotype
Lamarckian Algorithm ( Jean –Baptiste de Lamarck)
Phenotype Genotype

11. Project Goal
Study algorithms used to perform the searches and to calculate minimum energy
Discuss why GA+LS hybrid better than SA
Look at an example, i.e., dock a ligand to a protein molecule using latest AutoDock version

12. The Algorithms
Sue McClatchy

13. Simulated Annealing
Algorithm modeled after the cooling of a solution to form glass, though it’s better explained by crystal formation
Given a long enough cooling time, molecules will relax into their lowest energy state to form the largest crystals
Quick cooling - highly disordered system
Slow cooling - highly ordered crystal, with each molecule in its lowest energy state
Algorithm simulates either linear or proportional slow cooling

14. The SA Algorithm
Uses neighborhood operator N(s) to generate a set of solutions according to a fixed distribution
New solution compared to preceding solution, and is accepted if its energy is lower than that of previous solution
If new solution has higher energy, it is accepted probabilistically according to Boltzmann distribution (see figure above)
At high temperatures, many higher energy solutions will be accepted; at low temps., majority of probabilistic moves rejected
Boltzmann probability distribution = e exp(delta E/T) where delta E = energy difference between two solutions, T = temperature
Boltzmann finds p(of finding a system with energy E at temp T)

15. Pseudocode for SA Compute a random initial state s
n=0, x*n = s // initialize best solution to s and first state to 0
Repeat i = 1, 2, … // specify number of temperatures to try
Repeat j = 1, 2, …, mi // no. of steps to perform for each temp. Ti
Compute a neighbor s’ = N(s) // s’ = new solution from N(s)
if (f(s’) <= f(s)) then // if energy of s’ <= energy of s
s = s’ // accept new solution s’
if (f(s) < f(x*n)) then // if energy of new solution <
x*n = s // energy of best solution of
n = n // state n, replace best with new
endif
else // otherwise replace s with s’ using
s = s’ with probability e (f(s) - f(s’))/Ti // Boltzmann dist.
EndRepeat

16. How Genetic Algorithms Work - A Simple Example
Initial population of binary creatures having 6 “genes”
Each gene has two different alleles, either a 0 or a 1
Three operators: crossover, mutation and selection

17. Selection Selection based on a fitness function f(x)
Score
Selection based on a fitness function f(x)
This operator chooses those individuals with the lowest values
Those with higher values chosen with a very low probability 20 13 48 52

18. Crossover

19. Mutation

20. Replacement
# offsp
Score
Lower scoring individuals create more offspring, higher scoring ones create fewer or none at all
Offspring replace parental generation
“Elitism” function allows best individual from parent generation to persist, if it is a better solution than new individuals created
Cycle of selection, mutation, crossover and replacement repeated

21. Pseudocode for GA
Select an initial population set xi0 = {x10 , x20,…, xM0}
Determine fitness values f(xi0) for each individual
Repeat for g = 1, 2, … # of generations
Perform selection
Perform crossover with probability 
Perform mutation with probability 
Determine fitness f(xig) for new individuals
xg* = argmini=1,…M f(xig) and yg* = f(xg*)
Perform replacement
Until stopping criterion (# of generations) is reached

22. How GA works in AutoDock
Ligand’s “genes” are its x, y and z coordinates
These form a unit vector, which is given a random rotation angle between 0o and 360o to form a quaternion
Additional genes may represent torsion angles between bonds of the ligand

23. Mapping
In standard GA, the genotype (x,y,z coordinates plus rotation and any torsion angles) are mapped to the fitness function f(x)
The fitness function value corresponds to each individual’s phenotype
According to the right hand side of the figure, genotypes of parents with high f(x) values are mutated to form genotypes of children with lower f(x) values

24. Selection, Crossover & Mutation
Selection chooses ligands with the lowest fitness (energy) values
Crossover exchanges x, y, z coordinates, or rotations or torsions between these ligands
Example: Two ligands with xyz coordinates Abc and aBc Crossover results in new individuals with coordinates abc and ABc
Mutation operator mutates coordinate or other angle values by adding a random real number according to a Cauchy distribution, which is similar to a Gaussian but has thicker tails

25. Replacement
Individuals with better-than-average fitness receive proportionally more offspring
no= (fw – fi)/(fw - <f>),
fw != <f>
where
no= number of offspring
fi = fitness of individual (energy of ligand)
fw = fitness of worst individual in last g generations (typically 10)
<f> = mean fitness of population

26. Lamarckian Genetic Algorithm
According to left hand side of figure, LGA finds lowest fitness function (energy) values first, then maps these values to their respective genotypes
Genetic algorithm plus Solis and Wets local search
Better performance than either simulated annealing or genetic algorithm alone

27. The Application
Milind Misra

28. HIV-1 Protease and AHA006
HIV-1 Protease in complex with the cyclic sulfamide inhibitor, AHA006
Source: Protein Data Bank
Authors: K. Backbro, T. Unge
Exp. Method: X-ray Diffraction (2 Å res.)
Primary Citation: Backbro et al, J Med Chem 40 pp. 898 (1997)
Polymer Chains: A, B; Residues: 198; Atoms: 1632

29. Protein (HIV-1 Protease)
Ligand (AHA006)
(Source: PDB)

30. HIV-1 Protease dimer
(Rasmol)

31. Initial X-Ray crystallographic positions of protein and ligand
(SYBYL)

32. Docking Preparation – Ligand
Assign charges
Define rotatable bonds
Rename aromatic carbons
Merge non-polar hydrogens
Write .pdbq ligand file

33. Docking Preparation – Protein
Add essential hydrogens
Load charges
Merge lone-pairs
Add solvation parameters
Write .pdbqs protein file

34. Docking Preparation – Grid
AutoDock uses grid-based docking
Ligand-protein interaction energies are pre-calculated and then used as a look-up table during simulation
Grid maps are constructed based on atoms of interest in ligand (here CANOSH)

35. (AutoDockTools)

36. Docking – Simulated Annealing
Runs = 100
Cycles = 50
Initial Temp (RT) = 1,000
Temp reduction factor = .95
Linear temperature reduction
Translation reduction factor = 1
Quaternion reduction factor = 1
Torsional reduction factor = 1
# rotatable bonds = 12
Initial coordinates = Random
Initial quaternion = Random
Initial dihedrals = Random
Translation step = 2.0 Å
Quaternion step = 50 deg
Torsion step = 50 deg
Results:
100 different clusters
Energy range: to +64,000
Conformation #81:
Conformation #67:
Conformation #68:
Lowest energy conf not close to position but similar to original
Conf #67 closest to position and conformation of original ligand; higher energy
Conf #68 close to position but not conformation of original ligand; not as high energy

37. Original ligand conf
SA conformation #67
(SYBYL)

38. Original ligand conf
SA conformation #67
Close-up of previous
(SYBYL)

39. Original ligand conf
SA conformation #67
(SYBYL)

40. 100 Clustered SA Conformations
(gOpenMol)

41. Docking – Genetic Algorithm
Runs = 50
# Evaluations = 250,000
Population size = 50
Elitism count = 1
Mutation rate = 0.02
Crossover rate = 0.8
Window size = 10
Cauchy alpha = 0
Cauchy beta = 1
# rotatable bonds = 12
Initial coordinates = Random
Initial quaternion = Random
Initial dihedrals = Random
Translation step = 2.0 Å
Quaternion step = 50 deg
Torsion step = 50 deg
Results:
50 different clusters
Energy range: to
Conformation #39:
Conformation #9:
Lowest energy conformation overall closest to original ligand conformation
If only 10 runs had been used instead of 50, then conf #9 would have been the lowest energy conformation.

42. Docking – Local Search Runs = 50 Solis-Wets iterations = 300
Consecutive successes = 4
Consecutive failures = 4
Rho = 1
Lower bound on rho = 0.01
LS frequency = 0.06
# rotatable bonds = 12
Initial coordinates = Random
Initial quaternion = Random
Initial dihedrals = Random
Translation step = 2.0 Å
Quaternion step = 50 deg
Torsion step = 50 deg
Results:
18 different clusters
Energy range: to +215,200
Confs #20, 21, 22, 23:
Lowest energy conformation was most dissimilar to original ligand conformation
Better results could have been obtained by reducing the step sizes

43. Docking – Lamarckian GA
Runs = 10
Max # Evaluations = 250,000
Max # Generations = 27,000
Population size = 50
Elitism count = 1
Mutation rate = 0.02
Crossover rate = 0.8
Window size = 10
Cauchy alpha = 0
Cauchy beta = 1
Solis-Wets iterations = 300
Consecutive successes = 4
Consecutive failures = 4
Rho = 1
Lower bound on rho = 0.01
LS frequency = 0.06
* Gray options *
Results:
10 different clusters
Energy range: to –8.38
Conformation #7:
Lowest energy conformation fairly similar to original ligand conformation
If the number of runs was restricted to 10 for both GA and LGA, LGA would have generated the best structure

44. Original ligand conf Best GA conf Best LGA conf Best SA conf
Best LS conf
(SYBYL)

45. Original ligand conf
Best GA conf
Best LGA conf
Best SA conf
(SYBYL)

46. References
S.Kumar et.al. “Protein Flexibility and Electrostatic Interactions.” IBM Journal of Research and Development Vol45. No ¾ 2001.
G. Morris et.al. “Automated Docking Using a Lamarckian Genetic Algorithm and an Empirical Binding Free Energy Function.” Journal of Computational Chemistry, Vol. 19, No. 14, (1998)
C. Rosin et.al. “A Comparison of Global and Local Search Methods in Drug Docking.” UCSD CSE Technical Report #CS (1997)
C. A. Sotriffer et.al. “Automated Docking of Ligands to Antibodies: Methods and Applications.” Methods 20, (2000)
M. Vieth et.al. “Assessing Search Strategies for Flexible Docking.”
Practical Handbook of Genetic Algorithms. Edited by Lance Chambers
An Introduction to Genetic Algorithms. Melanie Mitchell.
Goodsell and Olson Prot. Struct. Func. Genet, 8, 195(1990).
Principals of Biochemistry: Lehninger
R. Durbin, S Eddy, A. Krogh, G. Mitchison Biological sequence analysis
Wm. E. Hart. “A Theoretical Comparison of Genetic Algorithms and Simulated Annealing” Sandia National Laboratories,