Docking protocol

Protocol summary

Pose generation

rDock uses a combination of stochastic and deterministic search techniques to generate low energy ligand poses. The standard docking protocol to generate a single ligand pose uses 3 stages of Genetic Algorithm search (GA1, GA2, GA3), followed by low temperature Monte Carlo (MC) and Simplex minimisation (MIN) stages.

Several scoring function parameters are varied between the stages to promote efficient sampling. The ECUT parameter of the \(S_{\text{inter}}\) vdW potential (defining the hardness of the intermolecular close range potential) is increased from 1 in the first GA stage (GA1) to a maximum of 120 in the MC and MIN stages, with intermediate values of 5 in GA2 and 25 in GA3. The functional form of the \(S_{\text{inter}}\) vdW potential is switched from a 4-8 potential in GA1 and GA2 to a 6-12 potential in GA3, MC and MIN.

In a similar fashion, the overall weight of the \(S_{\text{intra}}\) dihedral potential is ramped up from an initial value of 0.1 in GA1 to a final value of 0.5 in the MC and MIN stages, with intermediate values of 0.2 in GA2 and 0.3 in GA3. In contrast, the \(S_{\text{intra}}\) vdW parameters (as used for the ligand intramolecular potential) remain fixed at the final, hard values throughout the calculation (ECUT = 120, 6-12 potential).

Overall, we found this combination of parameter changes allows for efficient sampling of the very poor starting poses, whilst minimising the likelihood that poor ligand internal conformations are artificially favoured and trapped early in the search, and ensures that physically realistic potentials are used for final optimisation and analysis.

Genetic Algorithm

The GA chromosome consists of the ligand centre of mass (com), the ligand orientation, as represented by the quaternion (q) required to rotate the ligand principal axes from the Cartesian reference axes, the ligand rotatable dihedral angles, and the receptor rotatable dihedral angles. The ligand centre of mass and orientation descriptors, although represented by multiple floating point values (com.x, com.y, com.z, and q.s, q.x, q.y, q.z respectively), are operated on as intact entities by the GA mutation and crossover operators.

For so-called free docking, in which no external restraints other than the cavity penalty are imposed, the initial population is generated such that the ligand centre of mass is constrained to lie on a randomly selected grid point within the defined docking volume, and the ligand orientation and all dihedral angles are randomised completely. Mutations to the ligand centre of mass are by a random distance along a randomly oriented unit vector. Mutations to the ligand orientation are performed by rotating the ligand principal axes by a random angle around a randomly oriented unit vector. Mutations to the ligand and receptor dihedral angles are by a random angle. All mutation distances and angles are randomly selected from rectangular distributions of defined width.

A generation is considered to have passed when the number of new individuals created is equal to the population size. Instead of having a fixed number of generations, the GA is allowed to continue until the population converges. The population is considered converged when the score of the best scoring pose fails to improve by more than 0.1 over the last three generations. This allows early termination of poorly performing runs for which the initial population is not able to generate a good solution.

During initial testing the impact of a wide variety of GA parameters (Table 7) were explored on a small, representative set of protein-ligand complexes (3ptb, 1rbp, 1stp, 3dfr). We measured the frequency that the algorithm was able to find the experimental conformation, and the average run time. Optimum results were obtained with a steady state GA, roulette wheel selection, a single population of size (\(100 \times \text{(number of rotatable bonds)}\)), a crossover:mutation ratio of 40:60, and mutation distribution widths of ligand translation 2 Å, ligand rotation of 30 degrees and dihedral angle of 30 degrees. These parameters have been found to be generally robust across a wide variety of systems.

Table 7 Summary of GA parameter space explored, and final values

Parameter

Values Explored

Final Values

Number of populations

1, 2, 3, 4, 5

1

Selection operator

Roulette wheel, Rank

Roulette wheel

Mutation

Rectangular Cauchy

Rectangular

GA

Generational, Steady state

Steady state

Elitism

Yes, No

No

No of individuals modified in each generation

All values from 1 to population size

0.5 * population size

Population size

50, 75, 100, 125, 150, 200, 400, 800 * number of rotatable bonds

100 * number of rotatable bonds

Probability of choosing Crossover vs. Mutation

0.0, 0.05, 0.1 … 0.9, 0.95, 1.0

0.4

Torsion step

3, 12, 21, 30 degrees

30 degrees

Rotational step

3, 12, 21, 30 degrees

30 degrees

Translation step

0.1, 0.8, 1.4, 2.0 Å

2.0 Å

Monte Carlo

The method and parameters for low temperature Monte Carlo are similar to those described for phase 4 of the RiboDock simulated annealing search protocol. The overall number of trials is scaled according to the number of rotatable bonds in the ligand, from a minimum of 500 (\(N_{\text{rot}} = 0\)) to a maximum of 2000 (\(N_{\text{rot}} = 15\)). Maximum step sizes are: translation 0.1 Å, ligand rotation of 10 degrees and dihedral angle of 10 degrees. Step sizes are halved if the Metropolis acceptance rate falls below 0.25.

Simplex

The Nelder-Mead’s Simplex minimisation routine operates on the same chromosome representation as the GA, with the exception that the composite descriptors (centre of mass and orientation) are decomposed into their constituent floating point values.

Code implementation

Docking protocols are constructed at run-time (by RbtTransformFactory class) from docking protocol definition files (rDock .prm format). The default location for docking protocol files is $RBT_ROOT/data/scripts/. The docking protocol definition file defines the sequence of search algorithms that constitute a single docking run for a single ligand record. Each search algorithm component operates either on a single chromosome representing the system degrees of freedom, or on a population of such chromosomes. The chromosome is constructed (by RbtChromFactory class) as an aggregate of individual chromosome elements for the receptor, ligand and explicit solvent degrees of freedom, as defined by the flexibility parameters in the system definition file.

Table 8 Chromosome elements

Element

Defined by

Class

Length

Position

Centre of mass

RbtChromPositionElement

3

Orientation

Euler angles for principal axes

RbtChromPositionElement

3

Dihedral

Dihedral angle for rotatable bond

RbtChromDihedralElement

1 per bond

Occupancy

Explicit water occupancy state

RbtChromOccupancylElement

1 per water

Standard rDock docking protocol (dock.prm)

As stated above in this section, the standard rDock docking protocol consists of three phases of a Genetic Algorithm search, followed by low-temperature Monte Carlo and Simplex minimisation.

Table 9 Search algorithm components and C++ implementation classes

Component

Class

Operates on

Randomise population

RbtRandPopTransform

Chromosome population

Genetic algorithm search

RbtGATransform

Chromosome population

Monte Carlo simulated annealing

RbtSimAnnTransform

Single chromosome

Simplex minimisation

RbtSimplexTransform

Single chromosome

Null operation

RbtNullTransform

N/A

Table 10 Docking protocol data files

File

Description

score.prm

Calculates score only for initial conformation (standard scoring function)

scole_solv.prm

As above, but uses desolvation scoring function

minimise.prm

Simplex minimisation of initial conformation (standard scoring function)

minimise_solv.prm

As above, but uses desolvation scoring function

dock.prm

Full docking search (standard scoring function)

dock_solv.prm

As above, but uses desolvation scoring function

dock_grid.prm

Full docking search (standard scoring function, grid-based vdW term)

dock_solv_grid.prm

Full docking search (desolvation scoring function, grid-based vdW term)

By way of example, the dock.prm script is documented in detail. The other scripts are very similar.

SECTION SCORE
   INTER RbtInterIdxSF.prm
   INTRA RbtIntraSF.prm
   SYSTEM RbtTargetSF.prm
END_SECTION

Scoring Function The scoring function definition is referenced within the docking protocol definition file itself, in the SCORE section. This section contains entries for the INTER, INTRA and SYSTEM scoring function definition files.

SECTION SETSLOPE_1
   TRANSFORM RbtNullTransform
   # Dock with a high penalty for leaving the cavity
   WEIGHT@SCORE.RESTR.CAVITY 5.0
   # Gradually ramp up dihedral weight from 0.1-->0.5
   WEIGHT@SCORE.INTRA.DIHEDRAL 0.1
   # Gradually ramp up energy cut off for switching to quadratic
   ECUT@SCORE.INTER.VDW 1.0
   # Start docking with a 4-8 vdW potential
   USE 4_8@SCORE.INTER.VDW TRUE
   # Broader angular dependence
   DA1MAX@SCORE.INTER.POLAR 180.0
   # Broader angular dependence
   DA2MAX@SCORE.INTER.POLAR 180.0
   # Broader distance range
   DR12MAX@SCORE.INTER.POLAR 1.5
END_SECTION

Genetic Algorithm All sections that contain the TRANSFORM parameter are interpreted as a search algorithm component. The value of the TRANSFORM parameter is the C++ implementation class name for that transform. An RbtNullTransform can be used to send messages to the scoring function to modify key scoring function parameters in order to increase search efficiency. All parameter names that contain the @ symbol are interpreted as scoring function messages, where the string before the @ is the scoring function parameter name, the string after the @ is the scoring function term, and the parameter value is the new value for the scoring function parameter. Messages are sent blind, with no success feedback, as the docking protocol has no knowledge of the composition of the scoring function terms.

Here, we start the docking with a soft 4-8 vdW potential, a reduced dihedral potential, and extended polar ranges (distances and angles) for the intermolecular polar potential. These changes are all designed to aid sampling efficiency by not overpenalising bad contacts in the initial, randomised population, and by encouraging the formation of intermolecular hydrogen bonds.

SECTION RANDOM_POP
   TRANSFORM RbtRandPopTransform
   POP_SIZE 50
   SCALE_CHROM_LENGTH TRUE
END_SECTION

Creates an initial, randomised chromosome population. If SCALE_CHROM_LENGTH is false, the population is of fixed size, defined by POP_SIZE. If SCALE_CHROM_LENGTH is true, the population is proportional to the overall chromosome length, defined by POP_SIZE multiplied by the chromosome length.

SECTION GA_SLOPE1
   TRANSFORM RbtGATransform
   PCROSSOVER 0.4 # Prob. of crossover
   XOVERMUT TRUE # Cauchy mutation after each crossover
   CMUTATE FALSE # True = Cauchy; False = Rectang. for regular mutations
   STEP_SIZE 1.0 # Max relative mutation
END_SECTION

First round of GA.

SECTION SETSLOPE_3
   TRANSFORM RbtNullTransform
   WEIGHT@SCORE.INTRA.DIHEDRAL 0.2
   ECUT@SCORE.INTER.VDW 5.0
   DA1MAX@SCORE.INTER.POLAR 140.0
   DA2MAX@SCORE.INTER.POLAR 140.0
   DR12MAX@SCORE.INTER.POLAR 1.2
END_SECTION

Increases the ligand dihedral weight, increases the short-range intermolecular vdW hardness (ECUT), and decreases the range of the intermolecular polar distances and angles.

SECTION GA_SLOPE3
   TRANSFORM RbtGATransform
   PCROSSOVER 0.4 # Prob. of crossover
   XOVERMUT TRUE # Cauchy mutation after each crossover
   CMUTATE FALSE # True = Cauchy ; False = Rectang. for regular mutations
   STEP_SIZE 1.0 # Max relative mutation
END_SECTION

Second round of GA with revised scoring function parameters.

SECTION SETSLOPE_5
   TRANSFORM RbtNullTransform
   WEIGHT@SCORE.INTRA.DIHEDRAL 0.3
   ECUT@SCORE.INTER.VDW 25.0
   # Now switch to a convential 6-12 for final GA, MC, minimisation
   USE 4_8@SCORE.INTER.VDW FALSE
   DA1MAX@SCORE.INTER.POLAR 120.0
   DA2MAX@SCORE.INTER.POLAR 120.0
   DR12MAX@SCORE.INTER.POLAR 0.9
END_SECTION

Further increases the ligand dihedral weight, further increases the short-range intermolecular vdW hardness (ECUT), and further decreases the range of the intermolecular polar distances and angles. Also switches from softer 4-8 vdW potential to a harder 6-12 potential for final round of GA, MC and minimisation.

SECTION GA_SLOPE5
   TRANSFORM RbtGATransform
   PCROSSOVER 0.4 # Prob. of crossover
   XOVERMUT TRUE # Cauchy mutation after each crossover
   CMUTATE FALSE # True = Cauchy ; False = Rectang. for regular mutations
   STEP_SIZE 1.0 # Max relative mutation
END_SECTION

Final round of GA with revised scoring function parameters.

SECTION SETSLOPE_10
   TRANSFORM RbtNullTransform
   WEIGHT@SCORE.INTRA.DIHEDRAL 0.5 # Final dihedral weight matches SF file
   ECUT@SCORE.INTER.VDW 120.0 # Final ECUT matches SF file
   DA1MAX@SCORE.INTER.POLAR 80.0
   DA2MAX@SCORE.INTER.POLAR 100.0
   DR12MAX@SCORE.INTER.POLAR 0.6
END_SECTION

Resets all the modified scoring function parameters to their final values, corresponding to the values in the scoring function definition files. It is important that the final scoring function optimised by the docking search can be compared directly with the score-only and minimisation-only protocols, in which the scoring function parameters are not modified.

SECTION MC_10K
   TRANSFORM RbtSimAnnTransform
   START_T 10.0
   FINAL_T 10.0
   NUM_BLOCKS 5
   STEP_SIZE 0.1
   MIN_ACC_RATE 0.25
   PARTITION_DIST 8.0
   PARTITION_FREQ 50
   HISTORY_FREQ 0
END_SECTION

Monte Carlo Low temperature Monte Carlo sampling, starting from fittest chromosome from final round of GA.

SECTION SIMPLEX
   TRANSFORM RbtSimplexTransform
   MAX_CALLS 200
   NCYCLES 20
   STOPPING_STEP_LENGTH 10e-4
   PARTITION_DIST 8.0
   STEP_SIZE 1.0
   CONVERGENCE 0.001
END_SECTION

Minimisation Simplex minimisation, starting from fittest chromosome from low temperature Monte Carlo sampling.

SECTION FINAL
   TRANSFORM RbtNullTransform
   WEIGHT@SCORE.RESTR.CAVITY 1.0 # revert to standard cavity penalty
END_SECTION

Finally, we reset the cavity restraint penalty to 1. The penalty has been held at a value of 5 throughout the search, to strongly discourage the ligand from leaving the docking site.