Coulomb interactions between internal ionizable groups and surface charges in proteins

Victor KhangulovAugust 31, 2011

Institute in Multiscale Modeling of Biological interactionsJohns Hopkins University

Laboratory of Dr. Garcia-Moreno

Internal ionizable groups in proteins govern many biochemical processes

• Photoactivation

• Ion homeostasis

• H+ transport

• e- transfer

• Catalysis

Most ionizable residues are located on the protein surface.

Internal ionizable residues are responsible for energy transduction:

Can we engineer useful enzymes?

Structure-based Calculations:

• Overestimate electrostatic energies• Underestimate protein polarizability

+-

Background

• pKa values

• Dielectric constants

• Factors that determine pKa values of internal ionizable groups

• Measurement of pKa values of internal ionizable groups

• pKa values in SNase?

+

pKa = 10.4

pKa = 8.0

Shift in a pKa value is related to the Gibbs free energy (ΔG°)

ΔG° total

= 1.36 (10.4 – 8.0)

= 3.2 (kcal/mol)

Self and Coulomb Energies

+-

+𝐺𝑖 ,𝑖° (𝑘𝑐𝑎𝑙 /𝑚𝑜𝑙)=332𝑍2

2𝑟 𝑖𝑜𝑛 𝜀𝐺𝑖 , 𝑗° (𝑘𝑐𝑎𝑙 /𝑚𝑜𝑙)=

332𝑍 𝑖𝑍 𝑗

𝑟 𝑖 , 𝑗𝜀

Coulomb Energy Self Energy

ε εri,j

++εinεout

∆𝐺𝑖 , 𝑖°

+-

+εout εin

∆𝐺𝑖 , 𝑗°

What is a dielectric constant (ε)?

A macroscopic parameter that describes the polarizability of a material

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E

-

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Parallel plate capacitor

𝜀=𝐶

𝐶𝑉𝑎𝑐𝑢𝑢𝑚ε

0

80

40

20

10

30

50

60

70

Water

Vacuum (ε = 1)

Dry protein powder

Solid amides

DMSO

Dielectric Constants of Materials (2011). Clipper Controls

Liquid amides

Dependence of Coulomb energy on the dielectric constant (εp)

+-

ri,j = 3 Å

ri,j

ri,j = 12 Å

ε

pKa values of internal ionizable groups: Ideal Case

Background

L25K∆ ∆𝐺𝑝𝐻=∆∆𝐺𝑐−𝑅𝑇𝑙𝑛 [ 1+𝑒𝑧 ∙ 2.303 ∙ (𝑝𝐾𝑎

𝐷−𝑝𝐻 )

1+𝑒 𝑧 ∙ 2.303∙ (𝑝𝐾 𝑎𝑁 −𝑝𝐻 ) ]

Titration of Lys-25 in L25K variant in staphylococcal nuclease

Isom DG (2011). PNAS

A systematic study of pKa values of internal ionizable residues in staphylococcal nuclease

Isom DG (2011). PNAS

pKa values of internal groups are anomalous

Isom DG (2011). PNAS

Asp, Glu, and Lys at 25 internal positions in SNase

Measurement of pKa values: Ideal Case

Background

L25K • Assumption: Group behaves independently

• In “ideal” case, internal Lys does not affect pKa values of other ionizable groups

Isom DG (2011). PNAS

Measurement of pKa values: Non-Ideal Case

Isom DG (2011). PNAS13

Background

L25K

Background

T62K

Lys-25Lys-62

Goals of this study

• Determine the extent to which surface charges can be sensed inside a protein

• Examine the effect of surface charges on pKa values of internal ionizable groups

• Determine dielectric properties that govern communication between internal and surface charges in proteins

Variants of SNase where internal Lys is coupled to other ionizable groups

Isom DG (2011). PNAS

Factors that can affect pKa values in proteins

Coupling between internal and surface ionizable residues

Background

T62K

Shift in the pKa of one Lys only(Lys pKa

D = 10.4)

pKaN = 8

Coupling between internal and surface ionizable residues

Background

T62K

Shift in the pKa of Lys and His(Lys pKa

D = 10.4, His pKaD = 6)

His pKa,2N shifted down

Interactions between Lys-62 and surface residues

• What is the microenvironment of Lys-62?

• Which groups are interacting with Lys-62?

• What is the magnitude of these interactions?

• What are the structural consequences of ionization of Lys-62?

• Can these interactions be reproduced self-consistently with continuum electrostatics calculations?

Lys-62 is buried , 6.3 Å from Asp-21 and 8.4 Å from Asp-19

T62K (PHS)

PDB: 3DMU

Resolution: 1.80Å

R-work: 0.198

R-free: 0.255

D21N Substitution Affects pKa of Lys-62

Reference

T62K

Lys-62 pKa = 8.1 0.1

Isom DG (2011). PNAS

His-8

His-121

D21N Substitution Affects pKa of Lys-62

Reference D21N

T62KD21N/T62K

Lys-62 pKa = 8.1 0.1 Lys-62 pKa = 6.8 0.1

Isom DG (2011). PNAS

pKa = 8.10 ± 0.01(pKa = 8.1 ± 0.1 by linkage analysis)

T62K

Depressed pKa of Lys-62 confirmed by NMR spectroscopy

∆(1 H

N)

Che

mic

al S

hift

(pp

m)

24

pKa = 6.71 ± 0.03(pKa = 6.8 ± 0.1 by linkage analysis)

D21N/T62K

pH

∆(1 H

N)

Che

mic

al S

hift

(pp

m)

pKa of Lys-62 is depressed further in the D21N variant of SNase

Lys-62 reports on strong interaction with Asp-21 (1.9 kcal/mol)

+ +

+

- -pKa2 = 8.1

pKa1 = 6.7

∆G = 1.36 (pKa2 – pKa

1)

= 1.36 (8.1 – 6.7 )

= 1.9 kcal/mol

Coupling between Lys-62 and Asp-21

CBCGCO experiments probe the side chain carboxylic groups directly

Titration of Asp-21 shows dependence on the presence of Lys-62

Asp-21 in reference proteinpKa = 6.56 ± 0.02n = 2.00 ± 0.02

Asp-21 in T62KpKa = 4.17 ± 0.08n = 1.14 ± 0.13

Castañeda CA (2009). Proteins

Asp-21 reports on strong interaction with Lys-62 (3.3 kcal/mol)

+ +

+

- -

pKa2 = 6.6

pKa1 = 4.1

∆G = 1.36 (pKa2 – pKa

1)

= 1.36 (6.6 – 4.2 )

= 3.3 kcal/mol

Coupling between Lys-62 and Asp-21

Asymmetry in ∆Gij reported by Asp-21 and Lys-62

+ +

+

- -

pKa2 = 6.6

pKa1 = 4.1

∆Gi,j (Lys-62) = 1.9 kcal/mol

∆Gi,j (Asp-21) = 3.3 kcal/mol

Coupling between Lys-62 and Asp-21

pKa2 = 8.1

pKa1 = 6.7

Which ∆Gij correctly reflects coupling between Lys-62 and Asp-21?

Asp-21 Lys-62

HisAsp/Glu Lys

∆Gi,j (Asp-21) = 3.3 kcal/mol

∆Gi,j (Lys-62) = 1.9 kcal/mol

What other pKa values are affected by Lys-62?

T62KHis-8 -0.10 ± 0.02

Glu-10 -0.26 ± 0.13Asp-19 -Asp-21 -2.39 ± 0.01Asp-40 0.44 ± 0.10Glu-43 0.13 ± 0.04Glu-52 0.16 ± 0.08Glu-57 0.10 ± 0.09Glu-67 0.16 ± 0.12Glu-73 0.09 ± 0.02Glu-75 -Asp-77 -Asp-83 -Asp-95 -Glu-101 0.14 ± 0.10His-121 -0.09 ± 0.01Glu-122 0.03 ± 0.09Glu-129 0.14 ± 0.09Glu-135 -0.01 ± 0.08Glu-142 0.05 ± 0.04Asp-143 0.16 ± 0.10Asp-146 0.06 ± 0.05

ΔpKa between reference and variant protein with Lys-62

Is the interaction between Lys-62 and Asp-21 through protein or through solvent?

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-100 mM Salt 1M Salt

• Charge-charge interaction is shielded by high salt.

• pKa of Asp-21 returns to its “normal” value in the reference protein

Asp-21 in T62K pKa = 4.2

Case 1:ThroughProtein interaction

Case 2:ThroughSolvent interaction

• Interaction not shielded by high salt

• pKa of Asp-21 remains low

pKa = 4.2

pKa 4.2

pKa 6.1

Is the interaction between Lys-62 and Asp-21 through protein or through solvent?

pKa of Asp-21 in T62K

100 mM Salt 1M Salt

6.6 6.1pKa of Asp-21 in Reference protein

4.2 3.8

+

-Lys-62 interacts with Asp-21 through protein

34

Native structure is not perturbed by neutral Lys-62 in the crystal structure

Background (PHS)PDB: 1EY8Resolution: 1.75ÅR-work: 0.187R-free: 0.240

T62K (PHS)PDB: 3DMUResolution: 1.80ÅR-work: 0.198R-free: 0.255

Structure (as reported by TALOS+) is not perturbed by charged Lys

∆+PHS at pH 4.66

T62K at pH 4.52

Chemical Shifts:(C,CA,H,HN,HA)

Difference of > 30° in φ or ψBetween background and T62K

T62K residues in intermediateExchange.

Can structure-based calculations reproduce pKa values of Lys-62?

pKa in T62K: 8.1

pKa in D21N/T62K: 6.7

pKa in D19N/T62K: 7.5

Lys-62 experimental pKa values

Dielectric constant of 10.3 to11.5 reproduced pKa of Lys-62.

FDPB (UHBD), FULL/PARSE, Probe =1.4Å, Stern layer = 2.0ÅFitch CA (2002). Biophysical JournalKarp DA (2007). Biophysical Journal

Structure-based continuum calculations cannot reproduce pKa values and interactions

ΔGi,j(Asp-21 to Lys-62) = 1.9 kcal/mol

ΔGi,j(Asp-19 to Lys-62) = 0.8 kcal/mol

Calculated ΔGi,j value between Lys-62 and Asp-19 and Asp-21

εin required to reproduce ΔGi,j

6.7 (Asp-21 with Lys-62)> 9.5 (Asp-19 with Lys-62)

Conclusions

• Most pKa values are unaffected by Lys-62.

• There is a strong interaction between the internal Lys-62 and Asp-21.

• There is a weaker (but still strong) interaction between Lys-62 and Asp-19.

• The interaction between Lys-62 and Asp-21 appears to be through protein

• Therefore, the interaction between Lys-62 and Asp-21 is predominantly Coulomb in nature

• pKa and ΔGij cannot be reproduced with the same dielectric constant

Variants of SNase that where internal Lys titration is linked to other ionizable groups

Isom DG (2011). PNAS

pKa = 7.1 pKa = 7.2

pKa = 7.7

Internal Lys-34, Lys-36, and Lys-104 do not perturb the protein structure

Reference (3BDC)

F34K (3ITP)

L36K (3EJI)

L104K (3C1F)

Lys-34, 36, and 104 are buried in very different environments

F34K (3ITP) L36K (3EJI) L104K (3C1F)

Residues within 3.5 Å of buried Lys

Residues within 6.4 Å of buried Lys

Titration of His was virtually insensitive to the presence of internal charged Lys

His-8 His-121

Reference F34K L36K V104K

Largest shift of 0.3 pKa units was observed forHis-121 in F34K variant of SNase

Lys-34 has a weak interaction with Asp-21

Lys-34 and Asp-21 are 14 Å apart

Lys-34 with Asp-21pKa = 7.1 ± 0.1

Reference

F34K

Lys-34 has a weak interaction with Asp-21

Lys-34 and Asp-21 are 14 Å apart

Lys-34 with Asp-21pKa = 7.1 ± 0.1

Lys-34 w/o Asp-21pKa = 6.5 ± 0.6

0.8 kcal/mol

D21N

D21N/F34K

Titrations of Asp and Glu residues in the F34K variant

Reference F34K D21N/F34K

pKa = 6.60 ± 0.37

• Glu-10, Asp-77, Asp-82 and Glu-122 report on weak interactions with Lys-34

• Titration of Glu-122 may be reporting on the pKa of Lys-34 in D21N/F34K variant

• Since changes are globally distributed, interaction cannot be determined to be exclusively Coulomb in nature

What about other pKa values in F34K?

F34KHis-8 -0.16 ± 0.01

Glu-10 -0.04 ± 0.03Asp-19 0.31 ± 0.03Asp-21 -0.05 ± 0.01Asp-40 0.05 ± 0.10Glu-43 0.03 ± 0.04Glu-52 0.06 ± 0.08Glu-57 0.03 ± 0.09Glu-67 0.04 ± 0.12Glu-73 -0.04 ± 0.02Glu-75 -Asp-77 -Asp-83 -Asp-95 -0.04 ± 0.09Glu-101 0.19 ± 0.10His-121 0.28 ± 0.03Glu-122 -0.07 ± 0.08Glu-129 0.30 ± 0.09Glu-135 0.04 ± 0.08Glu-142 0.07 ± 0.05Asp-143 0.11 ± 0.02Asp-146 0.05 ± 0.01

ΔpKa between reference and variant protein with Lys-34

Ionization of Lys-34 contributes to globally distributed changes in the HSQC

Peaks not assigned

Peak broadening

Changes in Shifts > 1ppm

Chemical shifts were compared 0.5 pH unitsAbove and below pKa of Lys-34 (7.1)

Lys-36 exhibits high complexity in the ΔΔG vs. pH data

Lys-36 and Asp-21 are 6.3 Å apart

Lys-36 in L36KpKa = 7.2 ± 0.1

Reference

L36K

pKa values of Asp, Glu and His are not perturbed in L36K

L36KHis-8 -0.01 ± 0.01

Glu-10 -0.01 ± 0.04Asp-19

Asp-21

Asp-40 -0.05 ± 0.03Glu-43 0.00 ± 0.01Glu-52 -0.03 ± 0.02Glu-57 -0.02 ± 0.01Glu-67 -0.11 ± 0.04Glu-73 -0.16 ± 0.04Glu-75 -0.13 ± 0.12Asp-77 -Asp-83 -Asp-95 -Glu-101 0.09 ± 0.01His-121 0.01 ± 0.03Glu-122 -0.04 ± 0.02Glu-129 0.03 ± 0.01Glu-135 0.00 ± 0.02Glu-142 -0.09 ± 0.01Asp-143 -0.10 ± 0.03Asp-146 0.07 ± 0.03

ΔpKa between reference and variant protein with Lys-36

Lys-36 exhibits high complexity in the ΔΔG vs. pH data

Lys-36 and Asp-21 are 6.3 Å apart

Lys-36 in L36KpKa = 7.2 ± 0.1

Lys-36 in D21N/L36KpKa = 5.5 ± 1.1

D21N

D21N/L36K

2.3 kcal/mol

Ionization of Lys-36 does not perturb the structure of the protein

Peaks not assigned

Peak broadening

Changes in Shifts > 1ppm

Chemical shifts were compared 0.5 pH unitsAbove and below pKa of Lys-36 (7.2)

Lys-104 ΔΔG vs. pH data suggests significant interaction between Lys-62 and Asp-21

Lys-104 and Asp-21 are 9.3 Å apart

Lys-104 in V104KpKa = 7.7 ± 0.1

Reference

V104K

Lys-104 ΔΔG vs. pH data suggests significant interaction between Lys-62 and Asp-21

Lys-104 in V104KpKa = 7.7 ± 0.1

Lys-104 in D21N/V104KpKa = 6.10 ± 0.84

D21N

D21N/V104K

Lys-104 and Asp-21 are 9.3 Å apart

2.2 kcal/mol

Titration of Asp-21 reports no interaction with Lys-104

Reference V104K D21N/E101Q/V104K D21N/V104K/E122Q

• pKa of Asp-21 increased in V104K suggesting no direct interaction

• Titrations of Glu-101, Glu-122 and Glu-129 are consistent with weak interactions with Lys-104.

Only pKa of Asp-21 is perturbed in V104K

V104KHis-8 -0.01 ± 0.01

Glu-10 -Asp-19 -Asp-21 0.28 ± 0.04Asp-40 0.03 ± 0.01Glu-43 0.05 ± 0.01Glu-52 -0.04 ± 0.03Glu-57 0.11 ± 0.01Glu-67 0.09 ± 0.09Glu-73 0.00 ± 0.07Glu-75 -0.13 ± 0.12Asp-77 -Asp-83 -Asp-95 -Glu-101 0.03 ± 0.01His-121 0.01 ± 0.03Glu-122 -0.11 ± 0.02Glu-129 -0.24 ± 0.02Glu-135 0.03 ± 0.01Glu-142 -0.09 ± 0.01Asp-143 0.13 ± 0.01Asp-146 0.09 ± 0.01

ΔpKa between reference and variant protein with Lys-104

Ionization of Lys-104 contributes to local changes on the HSQC

Peaks not assigned

Peak broadening

Changes in Shifts > 1ppm

Chemical shifts were compared 0.5 pH unitsAbove and below pKa of Lys-104 (7.7)

Calculations exaggerate Coulomb interactions between internal and surface groups

F34K L36K V104K

pKa

ε ε ε

Coulomb contribution

Exp. pKa = 7.1

εapp= 8.0

Exp. pKa = 7.2 Exp. pKa = 7.7

εapp= 6.5 εapp= 3.5

FDPB (UHBD), FULL/PARSE, Probe =1.4Å, Stern layer = 2.0ÅFitch CA (2002). Biophysical JournalKarp DA (2007). Biophysical Journal

Calculations using the εapp that reproduced ΔGi,j , overerestimate shifts in pKa values.

Very strong interactions between groups are possible in ri,j < 10 Å

Conclusions

• Most interactions between internal and surface groups are very weak

• Strong interactions are possible in ri,j < 10Å

• pKa of internal groups can be modulated by surface charges

• pKa and ΔGi,j cannot be reproduced self-consistently using the same dielectric constant

ThanksBGME Lab

Dr. Carolyn FitchDr. Ana Damjanović

Aaron RobinsonBrian DoctrowAlfredo CaroPeregrine Bell-Upp

Dr. Daniel IsomDr. Michael HarmsDr. Michael ChimentiDr. Brian CannonDr. Carlos Castañeda

USNADr. Jamie Schlessman

Support Team

Jerry LevinChris AltizerJessica BaileyRanice CrosbyKen Rutledge

Jenkins Faculty

Dr. George RoseDr. Doug BarrickDr. Greg BowmanDr. Richard ConeDr. Juliette LecomteDr. Sarah WoodsonDr. Karen FlemingDr. Ananya Majumdar

Advisor

Dr. Bertrand García-Moreno E.

Analysis of CBCGCO Titration Curves

)(

)(

101

10)(

a

a

pKpHn

pKpHnAAH

obs pH

Castañeda CA et al. (2009) Molecular determinants of the pKa values of Asp and Glu residues in staphylococcal nuclease. Proteins 77:570-88. Available at: http://www.ncbi.nlm.nih.gov/pubmed/19533744.

Two-Site Binding Isotherm:

)2()(

)2()(2

211

211

10101

1010)(

aaa

aaa

pKpKpHpKpH

pKpKpHA

pKpHAHAH

obs pH

Modified Hill Equation: