Using waterswap to predict and understand binding affinities

Christopher Woods

Introduction

• Developer of software and algorithms to predict protein-ligand binding free energies

• Binding free energy measures binding affinity, can be directly related to Ki

• Developed “waterswap”. First-principles, calculation of absolute binding free energies

Protein

Ligand

+

Protein

Ligand

Complex

Protein

Ligand

Complex

ΔGbind

Protein

Ligand

Complex

ΔGbind

Biochemistry occurs in the aqueous phase

Prot

ein (

aq)

Liga

nd(a

q)

Prot

ein (

aq)

Liga

nd(a

q)

Wat

erC

ompl

ex(a

q)

Prot

ein (

aq)

Liga

nd(a

q)

Wat

erC

ompl

ex(a

q)

ΔGbind

Prot

ein (

aq)

Liga

nd(a

q)

Wat

erC

ompl

ex(a

q)

ΔGbind

Prot

ein (

aq)

Liga

nd(a

q)

Wat

erC

ompl

ex(a

q)

ΔGbind

Prot

ein (

aq)

Liga

nd(a

q)

Wat

erC

ompl

ex(a

q)

ΔGbind

•  Woods,&J&Chem&Phys,&Vol&134,&p054114,&2011&•  &h7p://dx.doi.org/10.1063/1.3519057&

Waterswap&Method&&Uses&the&fact&that&proteinJligand&binding&is&really&a&compeLLon&between&the&ligand&and&water&for&binding&to&the&protein&

Prot

ein:

Wat

er(a

q)Li

gand

(aq)

Prot

ein:

Wat

er(a

q)Li

gand

(aq)

Prot

ein:

Wat

er(a

q)Li

gand

(aq)

Wat

er(a

q)Pr

otei

n:Li

gand

(aq)

Prot

ein:

Wat

er(a

q)Li

gand

(aq)

Wat

er(a

q)Pr

otei

n:Li

gand

(aq)

ΔGbind

Prot

ein:

Wat

er(a

q)Li

gand

(aq)

Wat

er(a

q)Pr

otei

n:Li

gand

(aq)

ΔGbind

(*)

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

λ=0.0

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

λ=0.0

100%

0%

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

λ=0.2

80%

20%

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

λ=0.5

50%

50%

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

λ=0.8

20%

80%

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

λ=1.0

0%

100%

Perform Thermodynamic Integration (TI) along the Waterswap λ coordinate. This results, directly,

in the absolute binding free energy

!20$

!18$

!16$

!14$

!12$

!10$

!8$

!6$

!4$

!2$

0$0.0$ 0.2$ 0.4$ 0.6$ 0.8$ 1.0$

Free$Ene

rgy$/$kcal$m

ol01$

λ$

Perform Thermodynamic Integration (TI) along the Waterswap λ coordinate. This results, directly,

in the absolute binding free energy

!20$

!18$

!16$

!14$

!12$

!10$

!8$

!6$

!4$

!2$

0$0.0$ 0.2$ 0.4$ 0.6$ 0.8$ 1.0$

Free$Ene

rgy$/$kcal$m

ol01$

λ$

Perform Thermodynamic Integration (TI) along the Waterswap λ coordinate. This results, directly,

in the absolute binding free energy

!20$

!18$

!16$

!14$

!12$

!10$

!8$

!6$

!4$

!2$

0$0.0$ 0.2$ 0.4$ 0.6$ 0.8$ 1.0$

Free$Ene

rgy$/$kcal$m

ol01$

λ$

ΔGbind

How to use Waterswap?

Waterswap is built into

Sire, available from

http://siremol.org

Sire can be downloaded using

the links on this site...

...and there are full instructions on how to use

waterswap

…but,

• waterswap is easy to use…

• …but setting up a protein-ligand complex for simulation requires expert knowledge and is not trivial

• waterswap results depend on the quality of the input model

Test Application to Thrombin

Cl

NHO

N

R

O

CH3

H2

C

CH3

H2

C

CH2

CH3

H2

CHC

CH3

CH3

H2

C

CH2

CH

CH3

CH3

H2

C

H2

C

H2

C

CH2

H2

C

CH2

H2

C

CH2

1

2

3

4

5

6

7

8

9

10

R

20 30 40 50 60 70Dynamics

Dynamics + Waterswap

20 30 40 50 60 70Dynamics

20.crd 20.top

Dynamics + Waterswap

20 30 40 50 60 70Dynamics

Wat

ersw

ap

20.crd 20.top

Dynamics + Waterswap

20 30 40 50 60 70Dynamics

Wat

ersw

ap

�G20ns

20.crd 20.top

Dynamics + Waterswap

20 30 40 50 60 70Dynamics

Wat

ersw

ap

�G20ns

20.crd 20.top

30.crd 30.top

�G30ns

Wat

ersw

ap

Dynamics + Waterswap

20 30 40 50 60 70Dynamics

Wat

ersw

ap

�G20ns

20.crd 20.top

30.crd 30.top

�G30ns

Wat

ersw

ap40.crd 40.top

50.crd 50.top

60.crd 60.top

70.crd 70.top

�G40ns �G50ns �G60ns �G70ns

Wat

ersw

ap

Wat

ersw

ap

Wat

ersw

ap

Wat

ersw

ap

Dynamics + Waterswap

20 30 40 50 60 70Dynamics

Wat

ersw

ap

�G20ns

20.crd 20.top

30.crd 30.top

�G30ns

Wat

ersw

ap40.crd 40.top

50.crd 50.top

60.crd 60.top

70.crd 70.top

�G40ns �G50ns �G60ns �G70ns

Wat

ersw

ap

Wat

ersw

ap

Wat

ersw

ap

Wat

ersw

ap

Dynamics + Waterswap

< >

20 30 40 50 60 70Dynamics

Wat

ersw

ap

�G20ns

20.crd 20.top

30.crd 30.top

�G30ns

Wat

ersw

ap40.crd 40.top

50.crd 50.top

60.crd 60.top

70.crd 70.top

�G40ns �G50ns �G60ns �G70ns

Wat

ersw

ap

Wat

ersw

ap

Wat

ersw

ap

Wat

ersw

ap

Dynamics + Waterswap

< >

�Gbind

Cl

NHO

N

R

O

CH3

H2

C

CH3

H2

C

CH2

CH3

H2

CHC

CH3

CH3

H2

C

CH2

CH

CH3

CH3

H2

C

H2

C

H2

C

CH2

H2

C

CH2

H2

C

CH2

1

2

3

4

5

6

7

8

9

10

R

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5 -32 -30 -28 -26 -24 -22 -20

Exp

erim

ent /

kca

l mol

-1

Simulation / kcal mol-1

R2=0.82

1

2 3

4 10 8

5 6

7 9

!

Simulation should not try to compete with experiment.

!

The job of simulation is to provide inspiration and insight

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

Free Energy Decomposition

• As we integrate the total waterswap binding free energy...

• ...we also integrate free energy changes in the “protein” box and the “water” box

• Result are free energies that tell you if a ligand’s binding strength comes from a natural affinity for the protein, or an aversion to water

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5 -10 -8 -6 -4 -2

Exp

erim

ent /

kca

l mol

-1

Simulation / kcal mol-1

R2=0.14

1

2 3 4 8 10

6 7

5

9 -6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5 -26 -24 -22 -20 -18 -16 -14 -12

Exp

erim

ent /

kca

l mol

-1

Simulation / kcal mol-1

R2=0.84

1

2 3

4 5

6

10 8

7 9

Specificity driven by “water” box, i.e. the more hydrophobic the ligand, the less it

wants to be in the water box, and the more it wants to be in the protein box.

!

This shows that a “better” ligand is only better because it is more hydrophobic

Protein Box Water Box

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

Waterswap uses a λ-coordinate to swap a ligand and a water cluster between a protein box and a water box

Protein Box Water Box

E� = (1� �)[Eprotein:cluster

+ Ewater:ligand

]+

(�)[Eprotein:ligand

+ Ewater:cluster

]

Eresidue:cluster

Eresidue:ligand

Free Energy Decomposition

• As we integrate the total waterswap binding free energy...

• ...we also integrate the individual contributions from all of the binding site residues

• Result is a “free energy” that indicates whether the residue:ligand or residue:water complex is more stable

Ligand Water Cluster

Tota

l E

lect

rost

atic

va

n de

r Waa

ls

Phe227

Phe227

Phe227

Phe227

Phe227

Phe227

Ligand Water Cluster

Tota

l E

lect

rost

atic

va

n de

r Waa

ls

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

Ligand Water Cluster

Tota

l E

lect

rost

atic

va

n de

r Waa

ls

Phe227

Phe227

Phe227

Phe227

Phe227

Phe227

Ligand Water Cluster

Tota

l E

lect

rost

atic

va

n de

r Waa

ls

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

Asp189

Glu192

SUPPORTING INFORMATION

Rapid Decomposition and Visualisation of Protein-Ligand Binding Free Energies by Residue and by Water

Christopher J. Woods, Maturos Malaisree, Julien Michel, Ben Long, Simon McIntosh-Smith and Adrian J. Mulholland

Figure S1. Experimentally measured binding affinities for the 10 ligands studied in this work (m-chlorobenzyl) and for the ten benzamidine analogs. Binding affinities are taken from Muley et al., doi: 10.1021/jm9016416 (reference 32 in our paper).

Figure S2. Components of the waterswap free energy for selected residues as calculated using averages calculated over individual Monte Carlo iterations for the 20 ns snapshot of ligand 9 bound to thrombin.

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 100 200 300 400 500 600 700 800 900 1000

Free

Ene

rgy

/ kca

l mol

-1

Monte Carlo Iteration

His57

Lys60

Arg173

Ile174

Asp189

Ser195

Ser214

Trp215

Gly216

-9

-8

-7

-6

-5

-4

-3 0 1 2 3 4 5 6 7 8 9 10

Bin

ding

Aff

inity

/ kc

al m

ol-1

Ligand

m-chlorobenzyl

benzamidine

Replacing m-chlorobenzyl group with benzamidine group systematically improves binding of the ligands

Conclusion

• Waterswap enables direct, first-principles calculation of absolute binding free energies

• (but results depend on quality of model!)

• Free energies can be decomposed to per-residue and per-water components

• Aim is to provide inspiration and insight

Appendix

• waterswap is just one of our tools…

• Also have ligandswap, which calculates relative binding free energies by swapping one ligand with another

• Also have waterview, that lets you quickly visualise water dynamics in a binding site, e.g.

Acknowledgements• Organisers for inviting me and allowing me to talk

• You for your attention

• Dr. Maturos Malaisree (doing most of the work!)

• Dr. Julien Michel (discussions and providing thrombin test system)

• Prof. Adrian Mulholland, Simon McIntosh-Smith, Ben Long

• EPSRC and now BBSRC for funding

• eInfraStructureSouth for GPU compute

• ACRC (Bristol) for CPU compute

• Get the software at http://siremol.org

• Get in touch via Christopher.Woods@bristol.ac.uk

Identity Constraint

• How do we “identify” the cluster of water to be swapped with the drug?

• We developed the identity constraint. This is a new way of labelling water molecules in a simulation that is based on where the molecule is in space, rather than where it is located in the input coordinate file.

• Allows definition of water clusters without using restraints or external perturbations

Connect boxes to the same thermostat

Connect boxes to the same thermostatPlace identity points on the atoms of the ligand

Connect boxes to the same thermostatPlace identity points on the atoms of the ligand

Copy those points into the water box to identify a cluster

λ"="0.0" λ"="0.3" λ"="0.6" λ"="1.0"

•  Binding"free"energy"is"calculated"by"running"simula:ons"across"λ."Using"one"8>core"node,"one"free"energy"takes"24>48"hours"to"compute"

•  Implemented"in"Sire:"hHp://siremol.org""

•  Woods,"J"Chem"Phys,"Vol"134,"p054114,"2011"•  "hHp://dx.doi.org/10.1063/1.3519057"

Reflection Sphere• Only waters

whose centers are inside the sphere can move

• Any move that takes the center of a water outside the sphere is reflected back into the sphere

• This prevents waters from leaving

Grid Electrostatics• Interactions inside

reflection sphere calculated normally

• Interactions between reflection sphere atoms and atoms within buffer (dotted sphere) calculated normally

• Coulomb interactions between reflection sphere and fixed atoms outside the buffer are calculated using a pre-computed cubic grid

Grid Electrostatics• Use of pre-computed

grid means that there is no penalty to using a long-range electrostatic cutoff

• Compatible with advanced boundary conditions, such as reaction field or force-shifted cutoff

• Fine grid (0.5 Å) and tri-linear interpolation give high accuracy compared to direct calculation