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Drug Design and pH!Jan H. Jensen!

Department of Chemistry!University of Copenhagen!

http://propka.ki.ku.dk/~jhjensen!

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Drug Design and pH!Getting the protonation state right

on the ligand

and the protein!

The protonation state determines!

Charge and hydrogen bonding properties!

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pKa value => charge as a function of pH!

q(pH ) = 11+10 pH − pKa

5 1ACJ.pdb!

The protonation state determines charge and hydrogen bonding properties!

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Determining pKa values for ligands!

Experimental:!Spectroscopic feature vs pH!

pH!N

MR

Shi

ft!

Computational:!

Hammet-Taft rules !

PH+ P + H+ !

pKa = pKmodel + ρ σ ii

substituents

∑

pKa = ΔGrxn / RT ln(10)

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Ligand pKa prediction software using Hammet-Taft rules !

Epik!http://www.schrodinger.com/products/14/4/!

Marvin!http://www.chemaxon.com/marvin/sketch/index.jsp!

MoKa!http://www.moldiscovery.com/soft_moka.php!

ACD/pKa DB!http://www.acdlabs.com/products/phys_chem_lab/pka/!

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Drug Design and pH!Getting the protonation state right

on the ligand

and the protein !

The protonation state determines!

Charge and hydrogen bonding properties!

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Standard pKa values for residues !

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Picture of non-standard!Protonation state in active site!

Non standard pKa values for residues in proteins !

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Simple rules for pKa Predictions?!

pKa = 4.8!

pKa = 4.5!

pKa = 5.0!

pKa = 4.8 - 0.3!

pKa = 4.8 + 0.2!

pKa = 4.8 - 0.5 + 0.2!

AH A- + H+!pKa = ΔGrxn/1.36!

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�

pKa = pKamodel + ΔpKa

Desolv + ΔpKaHB + ΔpKa

Chg-Chg

Model pKa values:

C-End=3.20, Asp=3.80, Glu=4.50, His=6.50, Cys=9.00, Tyr=10.00,

N-End=8.0, Lys=10.50, Arg=12.50.

PROPKA1: Li, Robertson & Jensen Proteins 2005!(PROPKA3: Olsson, Rostkowski, Søndergaard, Jensen JCTC 2011)!

PropKa!

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DpKa: Hydrogen Bonding!! !∆pKa= -0.8 , if D < d1!

∆pKa= -0.8 (D-d2) / (d1-d2), if D < d2!! !!! !∆pKa= 0.0, if D > d2!∆pKa

D (Å)d1 d2

F0

0.00.0

O

O

D

HO

Li, Robertson & Jensen Proteins 2005!

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4.5 Å15.5 Å

N15.5Å=443∆pKa= +0.43

aNLocal=13∆pKa= +0.91

Asp102

Arg46

Leu103

b

-1.20

-1.20

-0.48-0.46

Asp148

Asp102

Arg46+0.73

-2.40

c

Example: Asp102 in RNase H1!

pKa = 3.8 + 1.3 - 3.3 - 1.7 = +0.1!

Exp = < 2.0

Li, Robertson & Jensen Proteins 2005!

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Ca 20,000 hits last 12 months! Included in PDB2PQR and Vega-ZZ (*)!

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PROPKA-VMD interface!

Rostkowski, Olsson, Søndergaard, Jensen BMC Struct. Biol. 2011!

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(a) Asp /Glu

-2

0

2

4

6

8

10

12

-2 0 2 4 6 8 10 12Experimental pKa values

PR

OP

KA

Pre

dic

tio

n

(b) Cys

2

4

6

8

10

12

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2 4 6 8 10 12 14Experimental pKa values

PR

OP

KA

Pre

dic

tio

n

(c) His

0

2

4

6

8

10

0 2 4 6 8 10Experimental pKa values

PR

OP

KA

Pre

dic

tio

n

(d) Lys

2

4

6

8

10

12

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2 4 6 8 10 12 14Experimental pKa values

PR

OP

KA

Pre

dic

tio

n

RMSD = 0.7!N = 210!

RMSD = 1.2!N = 41!

RMSD = 1.0!N = 11!

RMSD = 0.7!N = 24!

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P + L P·L

PH+ + L PH+·L

H+ H+Ka

f Kac

Kb+

Kb0

Kobs = Kb0 1+10 pKa

c − pH

1+10 pKaf − pH

pKa values can change upon ligand binding!

Kobs =[PiL]+ [PH + iL][P][L]+ [PH + ][L]

=[PiL][P][L]

1+ [PH+ iL]

[PiL]⎛⎝⎜

⎞⎠⎟

1+ [PH+ ]

[P]⎛⎝⎜

⎞⎠⎟

= Kb0

1+ [H+ ]

Kac

⎛⎝⎜

⎞⎠⎟

1+ [H+ ]

Kaf

⎛⎝⎜

⎞⎠⎟

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pKa values can change upon ligand binding!

Implication number 1:!

Inhibition constant is pH dependent!

Kobs = Kb0 1+10 pKa

c − pH

1+10 pKaf − pH

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pKa values can change upon ligand binding!

Implication number 2:!

Change in Ki wrt pH means !

change in protonation stateupon binding!

−∂ log(Kobs )

∂pH= qc − qf

Kobs = Kb0 qfqc

q = 11+10 pH − pKa

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pKa values can change upon ligand binding!

Implication number 3:!

Docking score using static

protonation state must be corrected!

�

ΔGb = −RT ln(Kb0) − RT ln 1+10pKa

c − pH

1+10pKaf − pH

⎛

⎝ ⎜

⎞

⎠ ⎟ = ΔGb

0 + ΔGb,pH0

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pKa values can change upon ligand binding!

Implication number 4:!

ΔH measured by calorimetry will be

buffer dependent and must be corrected!

ΔHcorrected = ΔHobs − (qc − qf )ΔHion

ΔHion is ionization enthalpy of buffer!

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Effect of Ligands: PROPKA 2.0!

�

pKa = pKamodel + ΔpKa

Desolv + ΔpKaHB + ΔpKa

Chg-Chg

PROPKA 2: Bas, Rogers & Jensen Proteins 2008!PROPKA3.1: Søndergaard & Jensen, in progress!

Atom typing!H-bond donor/acceptor!

Charged groups!Ligand ionizable groups/pKmodel!

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xxx.pdb!

pKmodel!

xxx.pka new_xxx.pdb!

PROPKA!

new_xxx.pdb!edit!

PROPKA!

new_xxx.pka!

Edit = !new pKmodel or!

new atom types!

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N29!

pKmodel!pKa!

C25!C91!

10.3!12.0!

3.2!

Experiment!

1K1L.pdb -> 1K1L.pka!

new_1K1L.pdb!

new_1K1L.pka!

27 Bas, Rogers & Jensen Proteins 2008!

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Summary!Implications for docking!

Protonation state of ligand can be estimated computationally!

Protonation states of active site residues are not!always “standard”!

Protonation states can change upon binding!

In which case docking score must be corrected!

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Questions Now?!

Questions Later?!

Leave a comment on!http://proteinsandwavefunctions.blogspot.com/2011/02/drug-design-and-ph.html!